메뉴 건너뛰기




Volumn 55, Issue 2, 2006, Pages 389-442

Operator theory on noncommutative varieties

Author keywords

Char acteristic function; Commutant lifting; Constrained shift; Dilation the ory; Fock space; Interpolation; Invariant subspace; Multivariable operator theory; Noncommutative variety; Poisson kernel; Row contraction; Von Neumann inequality; Wold decomposition

Indexed keywords


EID: 33646522037     PISSN: 00222518     EISSN: None     Source Type: Journal    
DOI: 10.1512/iumj.2006.55.2771     Document Type: Article
Times cited : (98)

References (39)
  • 1
    • 0034360839 scopus 로고    scopus 로고
    • Noncommutative interpolation and Poisson transforms
    • MR1749679 (2001i:47021)
    • A. ARIAS and G. POPESCU, Noncommutative interpolation and Poisson transforms, Israel J. Math. 115 (2000), 205-234. MR1749679 (2001i:47021)
    • (2000) Israel J. Math. , vol.115 , pp. 205-234
    • Arias, A.1    Popescu, G.2
  • 2
    • 34250491179 scopus 로고
    • Subalgebras of C*-algebras
    • MR0253059 (40 #6274)
    • W.B. ARVESON, Subalgebras of C*-algebras, Acta.Math. 123 (1969), 141-224. MR0253059 (40 #6274)
    • (1969) Acta.Math. , vol.123 , pp. 141-224
    • Arveson, W.B.1
  • 3
    • 0004089591 scopus 로고
    • An invitation to C*-algebras
    • Springer-Verlag, NewYork-Heidelberg, MR0512360 (58 #23621)
    • _, An invitation to C*-algebras, Graduate Texts in Math., vol. 39, Springer-Verlag, NewYork-Heidelberg, 1976. MR0512360 (58 #23621)
    • (1976) Graduate Texts in Math. , vol.39
  • 4
    • 0000326360 scopus 로고    scopus 로고
    • Subalgebras of C*-algebras III: Multivariable operator theory
    • MR1668582 (2000e:47013)
    • _, Subalgebras of C*-algebras III: Multivariable operator theory, Acta Math. 181 (1998), 159-228. MR1668582 (2000e:47013)
    • (1998) Acta Math. , vol.181 , pp. 159-228
  • 5
    • 0034366293 scopus 로고    scopus 로고
    • n]
    • MR1758582 (2003a:47013)
    • n], J. Reine Angew. Math. 522 (2000), 173-236. MR1758582 (2003a:47013)
    • (2000) J. Reine Angew. Math. , vol.522 , pp. 173-236
  • 6
    • 0037171107 scopus 로고    scopus 로고
    • Constrained von Neumann inequalities
    • MR1895563 (2003b:47017)
    • C. BADEA and G. GASSIER, Constrained von Neumann inequalities, Adv. Math. 166 (2002), 260-297, http://dx.doi.org/10.1006/aima.2001.2035. MR1895563 (2003b:47017)
    • (2002) Adv. Math. , vol.166 , pp. 260-297
    • Badea, C.1    Gassier, G.2
  • 7
    • 0036340615 scopus 로고    scopus 로고
    • A model theory for q-commuting contractive tuples
    • MR1905815 (2003c:47018)
    • B.V.R. BHAT and T. BHATTACHARYYA, A model theory for q-commuting contractive tuples, J. Operator Theory 47 (2002), 1551-1568, http://dx.doi.org/10.1007/BF01275511. MR1905815 (2003c:47018)
    • (2002) J. Operator Theory , vol.47 , pp. 1551-1568
    • Bhat, B.V.R.1    Bhattacharyya, T.2
  • 8
    • 1642399820 scopus 로고    scopus 로고
    • Standard noncommuting and commuting dilations of commuting tuples
    • MR2034318 (2005b:47011)
    • B.V.R. BHAT, T. BHATTACHARYYA, and S. DAY, Standard noncommuting and commuting dilations of commuting tuples, Trans. Amer. Math. Soc, 356 (2003), 1551-1568. MR2034318 (2005b:47011)
    • (2003) Trans. Amer. Math. Soc , vol.356 , pp. 1551-1568
    • Bhat, B.V.R.1    Bhattacharyya, T.2    Day, S.3
  • 9
    • 0040795146 scopus 로고
    • Models for n-tuples of noncommuting operators
    • MR0744917(85k:47019)
    • J.W. BUNGE, Models for n-tuples of noncommuting operators, J. Funct. Anal. 57 (1984), 21-30, http://dx.doi.org/10.1016/0022-1236(84)90098-3. MR0744917 (85k:47019)
    • (1984) J. Funct. Anal. , vol.57 , pp. 21-30
    • Bunge, J.W.1
  • 10
    • 0035592653 scopus 로고    scopus 로고
    • Isometric dilations of non-commuting finite rank n-tuples
    • MR1827819 (2002f:47010)
    • DAVIDSON. K.R., D.W. KRIBS, and M.E. SHPIGEL, Isometric dilations of non-commuting finite rank n-tuples, Canad. J. Math. 53 (2001), 506-545. MR1827819 (2002f:47010)
    • (2001) Canad. J. Math. , vol.53 , pp. 506-545
    • Davidson, K.R.1    Kribs, D.W.2    Shpigel, M.E.3
  • 11
    • 0032369135 scopus 로고    scopus 로고
    • The algebraic structure of non-commutative analytic Toeplitz algebras
    • MR1625750 (2001c:47082)
    • K.R. DAVIDSON and D. PITTS, The algebraic structure of non-commutative analytic Toeplitz algebras, Math. Ann. 311 (1998), 275-303, http://dx.doi.org/ 10.1007/s002080050188. MR1625750 (2001c:47082)
    • (1998) Math. Ann. , vol.311 , pp. 275-303
    • Davidson, K.R.1    Pitts, D.2
  • 12
    • 0032128697 scopus 로고    scopus 로고
    • Nevanlinna-Pick interpolation for noncommutative analytic Toeplitz algebras
    • MR1627901 (2000g:47016)
    • DAVIDSON. K.R. and D. PITTS, Nevanlinna-Pick interpolation for noncommutative analytic Toeplitz algebras, Integr. Equal. Oper.Th. 31 (1998), 321-337, http://dx.doi.org/10.1007/BF01195123. MR1627901 (2000g:47016)
    • (1998) Integr. Equal. Oper.Th. , vol.31 , pp. 321-337
    • Davidson, K.R.1    Pitts, D.2
  • 13
    • 84966242522 scopus 로고
    • A generalization of von Neumanns inequality to the complex ball
    • MR0480362 (80c:47010)
    • S. DRURY, A generalization of von Neumanns inequality to the complex ball, Proc. Amer. Math. Soc. 68 (1978), 300-304. MR0480362 (80c:47010)
    • (1978) Proc. Amer. Math. Soc. , vol.68 , pp. 300-304
    • Drury, S.1
  • 14
    • 0002451378 scopus 로고
    • Models for noncommuting operators
    • MR0671311 (84h:47010)
    • A.E. FRAZHO, Models for noncommuting operators, J. Funct. Anal. 48 (1982), 1-11, http://dx.doi.org/10.1016/0022-1236(82)90057-X.MR0671311 (84h:47010)
    • (1982) J. Funct. Anal. , vol.48 , pp. 1-11
    • Frazho, A.E.1
  • 15
    • 0035655203 scopus 로고    scopus 로고
    • The curvature invariant of a non-commuting N-tuple
    • MR1857801 (2003b:47013)
    • D. KRIBS, The curvature invariant of a non-commuting N-tuple, Integral Equations Operator Theory 41 (2001), 426-454, http://dx.doi.org/10.1007/ BF01202103. MR1857801 (2003b:47013)
    • (2001) Integral Equations Operator Theory , vol.41 , pp. 426-454
    • Kribs, D.1
  • 16
    • 0000611407 scopus 로고    scopus 로고
    • Invariant subspaces and Nevanlinna-Pick kernels
    • MR1800795(2002b:47006)
    • S. MCCULLOUGH and T.T. TRENT, Invariant subspaces and Nevanlinna-Pick kernels, J. Funct. Anal. 178 (2000), 226-249, http://dx.doi.org/10.1006/jfan. 2000.3664. MR1800795 (2002b:47006)
    • (2000) J. Funct. Anal. , vol.178 , pp. 226-249
    • McCullough, S.1    Trent, T.T.2
  • 17
    • 0001274397 scopus 로고    scopus 로고
    • Tensor algebras over C* -correspondences: Representations, dilations, and C*-envelopes
    • MR1648483 (99j:46066)
    • P. MUHLY and B. SOLEL, Tensor algebras over C* -correspondences: representations, dilations, and C*-envelopes, J. Funct. Anal. 158 (1998), 389-457, http://dx.doi.org/10.1006/jfan.1998.3294. MR1648483 (99j:46066)
    • (1998) J. Funct. Anal. , vol.158 , pp. 389-457
    • Muhly, P.1    Solel, B.2
  • 18
    • 0002997580 scopus 로고
    • Über beschränkte functionen, die in gegebenen punkten vorgeschribene werte annehmen
    • N. NEVANLINNA, Über beschränkte Functionen, die in gegebenen Punkten vorgeschribene Werte annehmen, Ann. Acad. Sci. Fenn. Ser A 13 (1919), 7-23.
    • (1919) Ann. Acad. Sci. Fenn. ser A , vol.13 , pp. 7-23
    • Nevanlinna, N.1
  • 19
    • 0003308653 scopus 로고
    • Similarity problems and completely bounded maps
    • Springer-Verlag, New York, MR1441076 (98d:47002)
    • G. PISIER, Similarity Problems and Completely Bounded Maps, Lect. Notes Math., vol. 1618, Springer-Verlag, New York, 1995. MR1441076 (98d:47002)
    • (1995) Lect. Notes Math. , vol.1618
    • Pisier, G.1
  • 20
    • 0000037512 scopus 로고
    • Models for infinite sequences of noncommuting operators
    • MR1033608 (91b:47025)
    • G. POPESCU, Models for infinite sequences of noncommuting operators, Acta. Sci. Math. (Szeged) 53 (1989), 355-368. MR1033608 (91b:47025)
    • (1989) Acta. Sci. Math. (Szeged) , vol.53 , pp. 355-368
    • Popescu, G.1
  • 21
    • 80955179187 scopus 로고
    • Isometric dilations for infinite sequences of noncommuting operators
    • MR0972704 (90c:47006)
    • _, Isometric dilations for infinite sequences of noncommuting operators, Trans. Amer. Math. Soc. 316 (1989), 523-536. MR0972704 (90c:47006)
    • (1989) Trans. Amer. Math. Soc. , vol.316 , pp. 523-536
  • 22
    • 0002100766 scopus 로고
    • Characteristic functions for infinite sequences of noncommuting operators
    • MR1026074 (91m:47012)
    • _, Characteristic functions for infinite sequences of noncommuting operators, J. Operator Theory 22 (1989), 51-71. MR1026074 (91m:47012)
    • (1989) J. Operator Theory , vol.22 , pp. 51-71
  • 23
    • 0000921434 scopus 로고
    • Multi-analytic operators and some factorization theorems
    • MR1017331 (90k:47019)
    • _, Multi-analytic operators and some factorization theorems, Indiana Univ. Math. J. 38 (1989), 693-710, http://dx.doi.org/10.1512/iumj.1989.38.38033. MR1017331 (90k:47019)
    • (1989) Indiana Univ. Math. J. , vol.38 , pp. 693-710
  • 24
    • 0001358149 scopus 로고
    • On intertwining dilations for sequences of noncommuting operators
    • MR1168596 (93e:47012)
    • _, On intertwining dilations for sequences of noncommuting operators, J. Math. Anal. Appl. 167 (1992), 382-402, http://dx.doi.org/10.1016/0022-247X(92) 90214-X. MR1168596 (93e:47012)
    • (1992) J. Math. Anal. Appl. , vol.167 , pp. 382-402
  • 25
    • 0000006932 scopus 로고
    • 1
    • MR1129595 (92k:47073)
    • 1, Math. Scand. 68 (1991), 292-304. MR1129595 (92k:47073)
    • (1991) Math. Scand. , vol.68 , pp. 292-304
  • 26
    • 0000694383 scopus 로고
    • Functional calculus for noncommuting operators
    • MR1342494 (96k:47025)
    • _, functional calculus for noncommuting operators, Michigan Math. J. 42 (1995), 345-356. MR1342494 (96k:47025)
    • (1995) Michigan Math. J. , vol.42 , pp. 345-356
  • 27
    • 0001925669 scopus 로고
    • Multi-analytic operators on Fock spaces
    • MR1348353 (96k:47049)
    • _, Multi-analytic operators on Fock spaces, Math. Ann. 303 (1995), 31-46, http://dx.doi.org/10.1007/BFO1460977. MR1348353 (96k:47049)
    • (1995) Math. Ann. , vol.303 , pp. 31-46
  • 28
    • 21344451348 scopus 로고    scopus 로고
    • Noncommutative disc algebras and their representations
    • MR1343719 (96k:47077)
    • _, Noncommutative disc algebras and their representations, Proc. Amer. Math. Soc. 124 (1996), 2137-2148, http://dx.doi.org/10.1090/S0002-9939-96-03514- 9. MR1343719 (96k:47077)
    • (1996) Proc. Amer. Math. Soc. , vol.124 , pp. 2137-2148
  • 29
    • 0000518649 scopus 로고    scopus 로고
    • Interpolation problems in several variables
    • MR1652931 (991:47028)
    • _, Interpolation problems in several variables, J. Math Anal. Appl. 227 (1998), 227-250, http://dx.doi.org/10.1006/jmaa.1998.6101. MR1652931 (991:47028)
    • (1998) J. Math Anal. Appl. , vol.227 , pp. 227-250
  • 30
    • 0033540185 scopus 로고    scopus 로고
    • Poisson transforms on some C*-algebras generated by isometries
    • MR1670202 (2000m:46117)
    • _, Poisson transforms on some C*-algebras generated by isometries, J. Funct. Anal. 161 (1999), 27-61, http://dx.doi.org/10.1006/jfan.1998.3346. MR1670202 (2000m:46117)
    • (1999) J. Funct. Anal. , vol.161 , pp. 27-61
  • 31
    • 23044533033 scopus 로고    scopus 로고
    • Commutant lifting, tensor algebras, and functional calculus
    • MR1880399 (2003f:47125)
    • _, Commutant lifting, tensor algebras, and functional calculus, Proc. Edinb. Math. Soc. 44 (2001), 389-406, http://dx.doi.org/10.1017/ S0013091598001059. MR1880399 (2003f:47125)
    • (2001) Proc. Edinb. Math. Soc. , vol.44 , pp. 389-406
  • 32
    • 0042198610 scopus 로고    scopus 로고
    • Curvature invariant for Hilbert modules over free semigroup algebras
    • MR1822685 (2002b:46097)
    • _, Curvature invariant for Hilbert modules over free semigroup algebras, Adv. Math. 158 (2001), 264-309, http://dx.doi.org/10.1006/aima.2000.1972. MR1822685 (2002b:46097)
    • (2001) Adv. Math. , vol.158 , pp. 264-309
  • 33
    • 0037138368 scopus 로고    scopus 로고
    • Central intertwining lifting, suboptimization, and interpolation in several variables
    • MR1887631 (2002m:47013)
    • _, Central intertwining lifting, suboptimization, and interpolation in several variables, J. Funct. Anal. 189 (2002), 132-154, http://dx.doi.org/10. 1006/jfan.2001.3861. MR1887631 (2002m:47013)
    • (2002) J. Funct. Anal. , vol.189 , pp. 132-154
  • 34
    • 0042854789 scopus 로고    scopus 로고
    • Similarity and ergodic theory of positive linear maps
    • MR1998608 (2004j:47009)
    • _, Similarity and ergodic theory of positive linear maps, J. Reine Angew. Math. 561 (2003), 87-129. MR1998608 (2004j:47009)
    • (2003) J. Reine Angew. Math. , vol.561 , pp. 87-129
  • 37
    • 84968466834 scopus 로고
    • Positive functions on C*-algebras
    • MR0069403 (16,1033b)
    • W.F. STINESPRING, Positive functions on C*-algebras, Proc. Amer. Math. Soc. 6 (1955), 211-216. MR0069403 (16,1033b)
    • (1955) Proc. Amer. Math. Soc. , vol.6 , pp. 211-216
    • Stinespring, W.F.1
  • 39
    • 84944815205 scopus 로고
    • Eine spectraltheorie für allgemeine operatoren eines unitären raumes
    • MR0043386 (13,254a)
    • J. VON NEUMANN, Eine Spectraltheorie für allgemeine Operatoren eines unitären Raumes, Math. Nachr. 4 (1951), 258-281. MR0043386 (13,254a)
    • (1951) Math. Nachr. , vol.4 , pp. 258-281
    • Von Neumann, J.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.