메뉴 건너뛰기




Volumn 248, Issue , 2005, Pages 323-362

Are unitarizable groups amenable?

Author keywords

Amenable; Herz Schur multiplier; Similarity problem; Uniformly bounded representation; Unitarizable

Indexed keywords


EID: 85028018694     PISSN: 07431643     EISSN: 2296505X     Source Type: Book Series    
DOI: 10.1007/3-7643-7447-0_8     Document Type: Chapter
Times cited : (32)

References (81)
  • 1
    • 0001993249 scopus 로고
    • The Burnside problem and identities in groups
    • Springer-Verlag, Berlin-New York
    • S. I. Adian. The Burnside problem and identities in groups. Ergebnisse der Mathematik 95. Springer-Verlag, Berlin-New York, 1979.
    • (1979) Ergebnisse Der Mathematik , vol.95
    • Adian, S.I.1
  • 2
    • 85027963332 scopus 로고
    • Izv. Akad. Nauk SSSR Ser
    • Random walks on free periodic groups. Izv. Akad. Nauk SSSR Ser. Mat. 46 (1982), 1139–1149.
    • (1982) Mat , vol.46 , pp. 1139-1149
  • 3
    • 51249186598 scopus 로고
    • Applications de la p-induction en analyse harmonique
    • J.-Ph. Anker. Applications de la p-induction en analyse harmonique, Comment. Math. Helv. 58 (1983), no. 4, 622–645.
    • (1983) Comment. Math. Helv. , vol.58 , Issue.4 , pp. 622-645
    • Anker, J.-P.1
  • 4
    • 0001852750 scopus 로고
    • A completely bounded characterization of operator algebras
    • D. Blecher. A completely bounded characterization of operator algebras. Math. Ann. 303 (1995), 227–240.
    • (1995) Math. Ann. , vol.303 , pp. 227-240
    • Blecher, D.1
  • 5
    • 84968504420 scopus 로고
    • Explicit constructions of universal operator algebras and applictions to polynomial factorization
    • D. Blecher and V. Paulsen. Explicit constructions of universal operator algebras and applictions to polynomial factorization. Proc. Amer. Math. Soc. 112 (1991), 839–850.
    • (1991) Proc. Amer. Math. Soc. , vol.112 , pp. 839-850
    • Blecher, D.1    Paulsen, V.2
  • 6
    • 0000671349 scopus 로고
    • A characterization of operator algebras
    • D. Blecher, Z. J. Ruan and A. Sinclair. A characterization of operator algebras. J. Funct. Anal. 89 (1990), 188–201.
    • (1990) J. Funct. Anal. , vol.89 , pp. 188-201
    • Blecher, D.1    Ruan, Z.J.2    Sinclair, A.3
  • 7
    • 84968504413 scopus 로고
    • Positive definite bounded matrices and a characterization of amenable groups
    • M. Bożejko. Positive definite bounded matrices and a characterization of amenable groups. Proc. Amer. Math. Soc. 95 (1985), 357–360.
    • (1985) Proc. Amer. Math. Soc. , vol.95 , pp. 357-360
    • Bożejko, M.1
  • 8
    • 0011912330 scopus 로고
    • ˙ Uniformly bounded representations of free groups
    • M. Bożejko.˙ Uniformly bounded representations of free groups. J. Reine Angew. Math. 377 (1987), 170–186.
    • (1987) J. Reine Angew. Math , vol.377 , pp. 170-186
    • Bożejko, M.1
  • 9
    • 85027974219 scopus 로고
    • Bożejko and G. Fendler. Herz-Schur multipliers and completely bounded multipliers of the Fourier algebra of a locally compact group. Boll. Unione Mat
    • Bożejko and G. Fendler. Herz-Schur multipliers and completely bounded multipliers of the Fourier algebra of a locally compact group. Boll. Unione Mat. Ital. (7) 3-A (1984), 297–302.
    • (1984) Ital. (7) 3-A , pp. 297-302
  • 10
    • 7044262472 scopus 로고
    • Choucroun. Analyse harmonique des groupes d’automorphismes d’arbres de Bruhat-Tits. (French) Mem. Soc
    • Choucroun. Analyse harmonique des groupes d’automorphismes d’arbres de Bruhat-Tits. (French) Mem. Soc. Math. France (N.S.) 58 (1994), 170 pp.
    • (1994) Math. France (N.S.) , vol.58 , pp. 170
  • 12
  • 14
    • 0000360209 scopus 로고
    • The Kunze-Stein phenomenon
    • The Kunze-Stein phenomenon. Ann. Math. 107 (1978), 209–234.
    • (1978) Ann. Math , vol.107 , pp. 209-234
  • 15
    • 85028007696 scopus 로고
    • Francesco Severi, Rome
    • 1982, 81–123, Ist. Naz. Alta Mat. Francesco Severi, Rome, 1983.
    • (1982) 81–123, Ist. Naz. Alta Mat , pp. 1983
  • 16
    • 0001353790 scopus 로고
    • Completely bounded multipliers of the Fourier algebra of a simple Lie group of real rank one
    • M. Cowling and U. Haagerup. Completely bounded multipliers of the Fourier algebra of a simple Lie group of real rank one. Invent. Math. 96 (1989), 507–549.
    • (1989) Invent. Math. , vol.96 , pp. 507-549
    • Cowling, M.1    Haagerup, U.2
  • 17
    • 0009063016 scopus 로고
    • Means for the bounded functions and ergodicity of the bounded representations of semi-groups
    • M. Day. Means for the bounded functions and ergodicity of the bounded representations of semi-groups. Trans. Amer. Math. Soc. 69 (1950), 276–291.
    • (1950) Trans. Amer. Math. Soc. , vol.69 , pp. 276-291
    • Day, M.1
  • 18
    • 0000025214 scopus 로고
    • ` and U. Haagerup. Multipliers of the Fourier algebras of some simple Lie groups and their discrete subgroups
    • J. de Cannière` and U. Haagerup. Multipliers of the Fourier algebras of some simple Lie groups and their discrete subgroups. Amer. J. Math. 107 (1985), 455–500.
    • (1985) Amer. J. Math , vol.107 , pp. 455-500
    • De Cannière, J.1
  • 19
    • 0000853787 scopus 로고
    • Les moyennes invariantes dans les semi-groupes et leurs applications
    • J. Dixmier. Les moyennes invariantes dans les semi-groupes et leurs applications. Acta Sci. Math. Szeged 12 (1950), 213–227.
    • (1950) Acta Sci. Math. Szeged , vol.12 , pp. 213-227
    • Dixmier, J.1
  • 21
    • 85028018321 scopus 로고
    • Effros and Z. J. Ruan. Multivariable multipliers for groups and their operator algebras. Operator theory: Operator algebras and applications, Part 1 (Durham, NH, 1988), 197–218
    • Amer. Math. Soc., Providence, RI
    • Effros and Z. J. Ruan. Multivariable multipliers for groups and their operator algebras. Operator theory: operator algebras and applications, Part 1 (Durham, NH, 1988), 197–218, Proc. Sympos. Pure Math., 51, 1, Amer. Math. Soc., Providence, RI, 1990.
    • (1990) Proc. Sympos. Pure Math , vol.1
  • 23
    • 33846285731 scopus 로고
    • A uniformly bounded representation associated to a free set in a discrete group
    • G. Fendler. A uniformly bounded representation associated to a free set in a discrete group. Colloq. Math. 59 (1990), no. 2, 223–229.
    • (1990) Colloq. Math , vol.59 , Issue.2 , pp. 223-229
    • Fendler, G.1
  • 28
    • 0000743985 scopus 로고
    • ∗ -algebras. Ann. of Math. (2) 118 (1983), 215–240.
    • (1983) Ann. of Math. (2) , vol.118 , pp. 215-240
  • 30
    • 0001610949 scopus 로고    scopus 로고
    • An example of a nonnuclear C -algebra, which has the metric approximation property
    • ∗ -algebra, which has the metric approximation property. Invent. Math. 50 279–293.
    • Invent. Math , vol.50 , pp. 279-293
  • 31
    • 0038280775 scopus 로고
    • Splitting in topological groups. Mem. Amer
    • Splitting in topological groups. Mem. Amer. Math. Soc. 43 (1963) 75 pp.
    • (1963) Math. Soc , vol.43 , pp. 75
  • 32
    • 0036384543 scopus 로고    scopus 로고
    • |g| is a coefficient of a uniformly bounded representation
    • |g| is a coefficient of a uniformly bounded representation. Fund. Math. 174 (2002), no. 1, 79–86.
    • (2002) Fund. Math , vol.174 , Issue.1 , pp. 79-86
    • Januszkiewicz, T.1
  • 33
    • 0036510204 scopus 로고    scopus 로고
    • Solution of a problem of Peller concerning similarity. J. Operator
    • N. Kalton and C. Le Merdy. Solution of a problem of Peller concerning similarity. J. Operator Theory 47 (2002), no. 2, 379–387.
    • (2002) Theory , vol.47 , Issue.2 , pp. 379-387
    • Kalton, N.1    Le Merdy, C.2
  • 34
    • 84968505289 scopus 로고
    • On the existence and irreducibility of certain series of representations
    • B. Kostant. On the existence and irreducibility of certain series of representations. Bull. Amer. Math. Soc. 75 (1969), 627–642.
    • (1969) Bull. Amer. Math. Soc , vol.75 , pp. 627-642
    • Kostant, B.1
  • 35
    • 0002607586 scopus 로고
    • Uniformly bounded representations and Harmonic Analysis of the 2 × 2 real unimodular group
    • R.A. Kunze and E. M. Stein. Uniformly bounded representations and Harmonic Analysis of the 2 × 2 real unimodular group. Amer. J. Math. 82 (1960), 1–62.
    • (1960) Amer. J. Math , vol.82 , pp. 1-62
    • Kunze, R.A.1    Stein, E.M.2
  • 36
    • 0010887395 scopus 로고
    • II. Analytic continuation of the principal series of representations of the n × n complex unimodular group. Amer
    • Uniformly bounded representations. II. Analytic continuation of the principal series of representations of the n × n complex unimodular group. Amer. J. Math. 83 (1961), 723–786.
    • (1961) J. Math , vol.83 , pp. 723-786
  • 37
    • 0001115464 scopus 로고
    • III. Intertwining operators for the principal series on semisimple groups. Amer
    • Uniformly bounded representations. III. Intertwining operators for the principal series on semisimple groups. Amer. J. Math. 89 (1967), 385–442.
    • (1967) J. Math , vol.89 , pp. 385-442
  • 38
    • 85027997841 scopus 로고
    • nAdvances in Math. 11 (1973), 1–71.
    • (1973) nAdvances in Math , vol.11 , pp. 1-71
  • 39
    • 84936690441 scopus 로고
    • Uniformly bounded representations of SL(2, C
    • R.L. Lipsman. Uniformly bounded representations of SL(2, C). Bull. Amer. Math. Soc. 73 (1967), 652–655.
    • (1967) Bull. Amer. Math. Soc , vol.73 , pp. 652-655
    • Lipsman, R.L.1
  • 40
    • 85027969227 scopus 로고
    • Uniformly bounded representations of SL(2, C). Amer. J. Math. 91 (1969), 47–66.
    • (1969) J. Math , vol.91 , pp. 47-66
  • 41
    • 84972567698 scopus 로고
    • ´ Sur les repr´esentations uniform´ement born´ees et le th´eor`eme de convolution de Kunze-Stein. (French) [Uniformly bounded representations and the Kunze-Stein convolution theorem
    • N. Lohoué.´ Sur les repr´esentations uniform´ement born´ees et le th´eor`eme de convolution de Kunze-Stein. (French) [Uniformly bounded representations and the Kunze-Stein convolution theorem] Osaka J. Math. 18 (1981), no. 2, 465–480.
    • (1981) Osaka J. Math , vol.18 , Issue.2 , pp. 465-480
    • Lohoué, N.1
  • 42
    • 0000411592 scopus 로고
    • Faltungsoperatoren auf gewissen diskreten Gruppen
    • M. Leinert. Faltungsoperatoren auf gewissen diskreten Gruppen. Studia Math. 52 (1974), 149–158.
    • (1974) Studia Math , vol.52 , pp. 149-158
    • Leinert, M.1
  • 43
    • 0003197518 scopus 로고
    • Properties of the Fourier algebra that are equivalent to amenability
    • V. Losert. Properties of the Fourier algebra that are equivalent to amenability. Proc. Amer. Math. Soc. 92 (1984), 347–354.
    • (1984) Proc. Amer. Math. Soc , vol.92 , pp. 347-354
    • Losert, V.1
  • 44
    • 85027963504 scopus 로고
    • M̷otkowski. Irreducible representations of free products of infinite groups. Colloq
    • M̷otkowski. Irreducible representations of free products of infinite groups. Colloq. Math. 69 (1995), no. 2, 193–211.
    • (1995) Ath. , vol.9 , pp. 93-211
  • 45
    • 34250084831 scopus 로고
    • Pytlik, R. Szwarc and A. Zappa. Equivalence of two series of spherical representations of a free group
    • A. M. Mantero, Pytlik, R. Szwarc and A. Zappa. Equivalence of two series of spherical representations of a free group. Ann. di Matematica pura ed applicata (IV) CLXV (1993), 23–28.
    • (1993) Ann. Di Matematica Pura Ed Applicata (IV) CLXV , pp. 23-28
    • Mantero, A.M.1
  • 46
    • 0038914081 scopus 로고
    • The Poisson transform and representations of a free group
    • A.M. Mantero and A. Zappa. The Poisson transform and representations of a free group. J. Funct. Anal. 51 (1983), no. 3, 372–399.
    • (1983) J. Funct. Anal. , vol.51 , Issue.3 , pp. 372-399
    • Mantero, A.M.1    Zappa, A.2
  • 47
    • 85027976827 scopus 로고
    • Springer, Berlin
    • p -convolution operators on a free group. 1982, 333–343, Lecture Notes in Math. 992, Springer, Berlin, 1983.
    • (1982) 333–343, Lecture Notes in Math. 992 , pp. 1983
  • 49
    • 84966232349 scopus 로고
    • Multipliers and asymptotic behaviour of the Fourier algebra of non amenable groups
    • C. Nebbia. Multipliers and asymptotic behaviour of the Fourier algebra of non amenable groups. Proc. Amer. Math. Soc. 84 (1982), 549–554.
    • (1982) Proc. Amer. Math. Soc. , vol.84 , pp. 549-554
    • Nebbia, C.1
  • 50
    • 85027978739 scopus 로고    scopus 로고
    • Simultaneous unitarizability and similarity problem
    • M. Nagisa and S. Wada. Simultaneous unitarizability and similarity problem. Sci-entiae Mathematicae (electr.) 2 (1999), no. 3, 255–261.
    • (1999) Sci-Entiae Mathematicae (Electr.) , vol.2 , Issue.3 , pp. 255-261
    • Nagisa, M.1    Wada, S.2
  • 51
    • 84860441014 scopus 로고
    • Shanskii. On the problem of the existence of an invariant mean on a group
    • A. Yu. Ol’shanskii. On the problem of the existence of an invariant mean on a group. Russian Math. Surveys 35 (1980), 180–181.
    • (1980) Russian Math. Surveys , vol.35 , pp. 180-181
    • Ol, A.Y.1
  • 52
    • 85028003787 scopus 로고
    • Kluwer Academic Publishers Group
    • Geometry of defining relations in groups. Kluwer Academic Publishers Group, Dordrecht, 1991.
    • (1991) Dordrecht
  • 54
    • 0242554667 scopus 로고    scopus 로고
    • Completely bounded maps and operator algebras. Cambridge Studies in Advanced Mathematics 78
    • V. Paulsen. Completely bounded maps and operator algebras. Cambridge Studies in Advanced Mathematics 78, Cambridge University Press, Cambridge, 2002
    • (2002) Cambridge University Press, Cambridge
    • Paulsen, V.1
  • 55
    • 0000302791 scopus 로고
    • Multilinear maps and tensor norms on operator systems
    • V. Paulsen and R. Smith. Multilinear maps and tensor norms on operator systems, J. Funct. Anal. 73 (1987), 258–276.
    • (1987) J. Funct. Anal. , vol.73 , pp. 258-276
    • Paulsen, V.1    Smith, R.2
  • 56
    • 0001304149 scopus 로고
    • Estimates of functions of power bounded operators on Hilbert space
    • V. Peller. Estimates of functions of power bounded operators on Hilbert space. J. Oper. Theory 7 (1982), 341–372.
    • (1982) J. Oper. Theory , vol.7 , pp. 341-372
    • Peller, V.1
  • 58
    • 85027996223 scopus 로고
    • Pitman
    • Amenable Banach algebras. Pitman, Longman, 1988.
    • (1988) Longman
  • 59
    • 0010963623 scopus 로고
    • Multipliers and lacunary sets in non amenable groups
    • G. Pisier. Multipliers and lacunary sets in non amenable groups. Amer. J. Math. 117 (1995), 337–376.
    • (1995) Amer. J. Math. , vol.117 , pp. 337-376
    • Pisier, G.1
  • 60
    • 85028004301 scopus 로고    scopus 로고
    • Expanded Edition
    • Similarity problems and completely bounded maps. Second, Expanded Edition. Springer Lecture Notes 1618 (2001).
    • (2001) Springer Lecture Notes , pp. 1618
  • 61
    • 0001315488 scopus 로고    scopus 로고
    • The similarity degree of an operator algebra
    • The similarity degree of an operator algebra. St. Petersburg Math. J. 10 (1999), 103–146.
    • (1999) St. Petersburg Math. J. , vol.10 , pp. 103-146
  • 62
    • 0034382506 scopus 로고    scopus 로고
    • The similarity degree of an operator algebra
    • The similarity degree of an operator algebra. II. Math. Zeit. 234 (2000), 53–81.
    • (2000) II. Math. Zeit , vol.234 , pp. 53-81
  • 63
    • 85027961529 scopus 로고
    • The volume of Convex Bodies and Banach Space Geometry
    • The volume of Convex Bodies and Banach Space Geometry. Cambridge University Press, 1989.
    • (1989) Cambridge University Press
  • 64
    • 0011699751 scopus 로고
    • Complex interpolation and regular operators between Banach lattices. Arch. Math. 62 (1994), 261–269.
    • (1994) Arch. Math , vol.62 , pp. 261-269
  • 65
    • 84875100749 scopus 로고    scopus 로고
    • 1 and power bounded operators. Colloq. Math. 88 (2001), no. 1, 57–73.
    • (2001) Colloq. Math , vol.88 , Issue.1 , pp. 57-73
  • 66
    • 0032128978 scopus 로고    scopus 로고
    • Op. Th. 31 (1998), 353–370.
    • (1998) Op. Th , vol.31 , pp. 353-370
  • 67
    • 85027982349 scopus 로고    scopus 로고
    • Cambridge Univ. Press., Cambridge
    • Notes 294, Cambridge Univ. Press., Cambridge, 2003.
    • (2003) Notes , vol.294
  • 68
    • 0000333901 scopus 로고
    • Cocycles on trees. J. Operator
    • M. Pimsner. Cocycles on trees. J. Operator Theory 17 (1987), no. 1, 121–128.
    • (1987) Theory , vol.17 , Issue.1 , pp. 121-128
    • Pimsner, M.1
  • 69
    • 85021164920 scopus 로고
    • Spherical functions and uniformly bounded representations of free groups
    • T. Pytlik. Spherical functions and uniformly bounded representations of free groups. Studia Math. 100 (1991), no. 3, 237–250.
    • (1991) Studia Math , vol.100 , Issue.3 , pp. 237-250
    • Pytlik, T.1
  • 70
    • 0010592649 scopus 로고
    • An analytic family of uniformly bounded representations of free groups
    • T. Pytlik and R. Szwarc. An analytic family of uniformly bounded representations of free groups. Acta Math. 157 (1986), no. 3–4, 287–309.
    • (1986) Acta Math , vol.157 , Issue.34 , pp. 287-309
    • Pytlik, T.1    Szwarc, R.2
  • 72
    • 70450227227 scopus 로고
    • Unitary and uniformly bounded representations of the two by two unimodular group over local fields
    • P. J. Sally Jr. Unitary and uniformly bounded representations of the two by two unimodular group over local fields. Amer. J. Math. 90 (1968), 406–443.
    • (1968) Amer. J. Math , vol.90 , pp. 406-443
    • Sally, P.J.1
  • 73
    • 84968513331 scopus 로고
    • Uniformly bounded representations of the universal covering group of SL(2, R). Bull. Amer
    • Uniformly bounded representations of the universal covering group of SL(2, R). Bull. Amer. Math. Soc. 72 (1966), 269–273.
    • (1966) Math. Soc , vol.72 , pp. 269-273
  • 74
    • 3142701331 scopus 로고    scopus 로고
    • Measurable Schur multipliers and completely bounded multipliers of the Fourier algebras
    • N. Spronk. Measurable Schur multipliers and completely bounded multipliers of the Fourier algebras. Proc. London Math. Soc. 89 (2004), 161–192.
    • (2004) Proc. London Math. Soc , vol.89 , pp. 161-192
    • Spronk, N.1
  • 75
    • 84973997508 scopus 로고
    • Banach algebras associated with spherical representations of the free group
    • R. Szwarc. Banach algebras associated with spherical representations of the free group. Pacific J. Math. 143 (1990), no. 1, 201–207.
    • (1990) Pacific J. Math , vol.143 , Issue.1 , pp. 201-207
    • Szwarc, R.1
  • 76
    • 77954595203 scopus 로고
    • Matrix coefficients of irreducible representations of free products of groups. Studia Math. 94 (1989), no. 2, 179–185.
    • (1989) Studia Math , vol.94 , Issue.2 , pp. 179-185
  • 78
    • 0001436249 scopus 로고
    • Cocycles d’arbres et représentations´ uniform´ement born´ees. (French) C. R. Acad. Sci. Paris S´r. I
    • A. Valette. Cocycles d’arbres et représentations´ uniform´ement born´ees. (French) C. R. Acad. Sci. Paris S´r. I Math. 310 (1990), no. 10, 703–708.
    • (1990) Math , vol.310 , Issue.10 , pp. 703-708
    • Valette, A.1
  • 79
    • 0039178948 scopus 로고
    • Les représentations´ uniform´ement born´ees associ´ees `a un arbre r´eel. (French) [Uniformly bounded representations associated with a real tree] Algebra, groups and geometry
    • Les représentations´ uniform´ement born´ees associ´ees `a un arbre r´eel. (French) [Uniformly bounded representations associated with a real tree] Algebra, groups and geometry. Bull. Soc. Math. Belg. Sér.´ A 42 (1990), 747–760.
    • (1990) Bull. Soc. Math. Belg. Sér , vol.42 , pp. 747-760
  • 80
    • 0002834910 scopus 로고
    • On an inequality of von Neumann and an application of the metric theory of tensor products to Operators Theory
    • N. Varopoulos. On an inequality of von Neumann and an application of the metric theory of tensor products to Operators Theory. J. Funct. Anal. 16 (1974), 83–100.
    • (1974) J. Funct. Anal , vol.16 , pp. 83-100
    • Varopoulos, N.1
  • 81
    • 84972576813 scopus 로고
    • ´ An analytic family of uniformly bounded representations of a free product of discrete groups
    • J. Wysoczański.´ An analytic family of uniformly bounded representations of a free product of discrete groups. Pacific J. Math. 157 (1993), no. 2, 373–387.
    • (1993) Pacific J. Math , vol.157 , Issue.2 , pp. 373-387
    • Wysoczański, J.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.