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Volumn 275, Issue 4, 2018, Pages 869-891

A dichotomy property for locally compact groups

Author keywords

I0 set; Locally compact group; Sidon set; Weak topology

Indexed keywords


EID: 85045020871     PISSN: 00221236     EISSN: 10960783     Source Type: Journal    
DOI: 10.1016/j.jfa.2018.03.013     Document Type: Article
Times cited : (4)

References (48)
  • 1
    • 84972582803 scopus 로고
    • Non-abelian Pontriagin duality
    • Akemann, Charles A., Walter, Martin E., Non-abelian Pontriagin duality. Duke Math. J. 39 (1972), 451–463.
    • (1972) Duke Math. J. , vol.39 , pp. 451-463
    • Akemann, C.A.1    Walter, M.E.2
  • 2
    • 0001464247 scopus 로고
    • A note on compact representations and almost periodicity in topological groups
    • Alfsen, E.M., Holm, P., A note on compact representations and almost periodicity in topological groups. Math. Scand., 1962.
    • (1962) Math. Scand.
    • Alfsen, E.M.1    Holm, P.2
  • 3
    • 0011570387 scopus 로고
    • Bohr compactifications of a locally compact Abelian group I
    • Anzai, H., Kakutani, S., Bohr compactifications of a locally compact Abelian group I. Proc. Imp. Acad., 1943.
    • (1943) Proc. Imp. Acad.
    • Anzai, H.1    Kakutani, S.2
  • 4
    • 84866790956 scopus 로고    scopus 로고
    • Kazhdan's Property
    • Cambridge University Press Cambridge
    • Bekka, Bachir, de la Harpe, Pierre, Valette, Alain, Kazhdan's Property. 2008, Cambridge University Press, Cambridge.
    • (2008)
    • Bekka, B.1    de la Harpe, P.2    Valette, A.3
  • 5
    • 84972514508 scopus 로고
    • Locally compact topologies on a group and the corresponding continuous irreducible representations
    • Bichteler, K., Locally compact topologies on a group and the corresponding continuous irreducible representations. Pacific J. Math. 31 (1969), 583–593.
    • (1969) Pacific J. Math. , vol.31 , pp. 583-593
    • Bichteler, K.1
  • 6
    • 84934989432 scopus 로고
    • Compact sets of first baire class
    • Bourgain, J., Compact sets of first baire class. Bull. Soc. Math. Belg. 29:2 (1977), 135–143.
    • (1977) Bull. Soc. Math. Belg. , vol.29 , Issue.2 , pp. 135-143
    • Bourgain, J.1
  • 7
    • 0010761868 scopus 로고
    • Pointwise compact sets of Baire-measurable functions
    • Bourgain, J., Fremlin, D.H., Talagrand, M., Pointwise compact sets of Baire-measurable functions. Amer. J. Math. 100:4 (1978), 845–886.
    • (1978) Amer. J. Math. , vol.100 , Issue.4 , pp. 845-886
    • Bourgain, J.1    Fremlin, D.H.2    Talagrand, M.3
  • 8
    • 23044523891 scopus 로고    scopus 로고
    • The Lindelöf property and fragmentability
    • Cascales, B., Namioka, I., Vera, G., The Lindelöf property and fragmentability. Proc. Amer. Math. Soc. 128:11 (2000), 3301–3309.
    • (2000) Proc. Amer. Math. Soc. , vol.128 , Issue.11 , pp. 3301-3309
    • Cascales, B.1    Namioka, I.2    Vera, G.3
  • 9
    • 79958810403 scopus 로고    scopus 로고
    • Subalgebras generated by extreme points in Fourier–Stieltjes algebras of locally compact groups
    • Cheng, Michael Yin-Hei, Subalgebras generated by extreme points in Fourier–Stieltjes algebras of locally compact groups. Stud. Math. 202:3 (2011), 289–302.
    • (2011) Stud. Math. , vol.202 , Issue.3 , pp. 289-302
    • Cheng, M.Y.-H.1
  • 10
    • 84881610985 scopus 로고    scopus 로고
    • On the subalgebra of a Fourier–Stieltjes algebra generated by pure positive definite functions
    • Cheng, Yin-Hei, Forrest, Brian E., Spronk, Nico, On the subalgebra of a Fourier–Stieltjes algebra generated by pure positive definite functions. Monatsh. Math. 171:3–4 (2013), 305–314.
    • (2013) Monatsh. Math. , vol.171 , Issue.3-4 , pp. 305-314
    • Cheng, Y.-H.1    Forrest, B.E.2    Spronk, N.3
  • 11
    • 0002829318 scopus 로고
    • Minimally weakly almost periodic groups
    • Chou, Ching, Minimally weakly almost periodic groups. J. Funct. Anal. 36 (1980), 1–17.
    • (1980) J. Funct. Anal. , vol.36 , pp. 1-17
    • Chou, C.1
  • 12
    • 84966217406 scopus 로고
    • Joint Continuity of separately continuous functions
    • Christensen, J.P.R., Joint Continuity of separately continuous functions. Proc. Amer. Math. Soc. 82:3 (1981), 455–461.
    • (1981) Proc. Amer. Math. Soc. , vol.82 , Issue.3 , pp. 455-461
    • Christensen, J.P.R.1
  • 13
    • 0011575516 scopus 로고
    • The Bohr compactification, modulo a metrizable subgroup
    • Comfort, W.W., Trigos-Arrieta, F.J., Wu, T.-S., The Bohr compactification, modulo a metrizable subgroup. Fund. Math. 143 (1993), 119–136.
    • (1993) Fund. Math. , vol.143 , pp. 119-136
    • Comfort, W.W.1    Trigos-Arrieta, F.J.2    Wu, T.-S.3
  • 14
    • 0003687916 scopus 로고
    • C*-Algèbres et leurs representations
    • Gauthier-Villars & Cie, Éditeur-Imprimeur Paris
    • Dixmier, J., C*-Algèbres et leurs representations. 1964, Gauthier-Villars & Cie, Éditeur-Imprimeur, Paris.
    • (1964)
    • Dixmier, J.1
  • 16
    • 84959771432 scopus 로고
    • A strong duality theorem for separable locally compact groups
    • Ernest, J., A strong duality theorem for separable locally compact groups. Trans. Amer. Math. Soc. 156 (1971), 287–307.
    • (1971) Trans. Amer. Math. Soc. , vol.156 , pp. 287-307
    • Ernest, J.1
  • 17
    • 0000724626 scopus 로고
    • L'algèbre de Fourier d'un groupe localement compact
    • Eymard, P., L'algèbre de Fourier d'un groupe localement compact. Bull. Soc. Math. France 92 (1964), 181–236.
    • (1964) Bull. Soc. Math. France , vol.92 , pp. 181-236
    • Eymard, P.1
  • 18
    • 84972296012 scopus 로고
    • A compact space having the cardinality of the continuum with no convergent sequences
    • Fedorčuk, V.V., A compact space having the cardinality of the continuum with no convergent sequences. Math. Proc. Cambridge Philos. Soc. 81:2 (1977), 177–181.
    • (1977) Math. Proc. Cambridge Philos. Soc. , vol.81 , Issue.2 , pp. 177-181
    • Fedorčuk, V.V.1
  • 19
    • 52449143175 scopus 로고
    • Insiemi lacunari nei gruppi non commutativi
    • Figa-Talamanca, Alessandro, Insiemi lacunari nei gruppi non commutativi. Rend. Semin. Mat. Fis. Milano 47 (1977), 45–59.
    • (1977) Rend. Semin. Mat. Fis. Milano , vol.47 , pp. 45-59
    • Figa-Talamanca, A.1
  • 20
    • 0013503172 scopus 로고    scopus 로고
    • The concept of boundedness and the Bohr compactification of a MAP abelian group
    • Galindo, J., Hernández, S., The concept of boundedness and the Bohr compactification of a MAP abelian group. Fund. Math. 159:3 (1999), 195–218.
    • (1999) Fund. Math. , vol.159 , Issue.3 , pp. 195-218
    • Galindo, J.1    Hernández, S.2
  • 21
    • 4444234577 scopus 로고    scopus 로고
    • Interpolation sets and the Bohr topology of locally compact groups
    • Galindo, J., Hernández, S., Interpolation sets and the Bohr topology of locally compact groups. Adv. Math. 188 (2004), 51–68.
    • (2004) Adv. Math. , vol.188 , pp. 51-68
    • Galindo, J.1    Hernández, S.2
  • 22
    • 0001535687 scopus 로고
    • Uniform boundedness for groups
    • Glicksberg, I., Uniform boundedness for groups. Canad. J. Math. 14 (1962), 269–276.
    • (1962) Canad. J. Math. , vol.14 , pp. 269-276
    • Glicksberg, I.1
  • 23
    • 84910621668 scopus 로고    scopus 로고
    • Interpolation and Sidon Sets for Compact Groups
    • Graham, C., Hare, K.E., Interpolation and Sidon Sets for Compact Groups. 2013.
    • (2013)
    • Graham, C.1    Hare, K.E.2
  • 24
    • 0037658193 scopus 로고
    • Almost periodic extensions of functions
    • Hartman, S., Ryll-Nardzewski, C., Almost periodic extensions of functions. Colloq. Math. 12:1 (1964), 29–39.
    • (1964) Colloq. Math. , vol.12 , Issue.1 , pp. 29-39
    • Hartman, S.1    Ryll-Nardzewski, C.2
  • 25
    • 85047765016 scopus 로고    scopus 로고
    • Equicontinuity criteria for metric-valued sets of continuous functions, Topology and its Applications, Pending.
    • S. Hernández, L. Tárrega, M. Ferrer, Equicontinuity criteria for metric-valued sets of continuous functions, Topology and its Applications, Pending.
    • Hernández, S.1    Tárrega, L.2    Ferrer, M.3
  • 26
    • 33750076335 scopus 로고    scopus 로고
    • Some new results on the Chu duality of discrete groups
    • Hernández, S., Wu, Ta-Sun, Some new results on the Chu duality of discrete groups. Monatsh. Math. 149:3 (2006), 215–232.
    • (2006) Monatsh. Math. , vol.149 , Issue.3 , pp. 215-232
    • Hernández, S.1    Wu, T.-S.2
  • 27
    • 0003962321 scopus 로고
    • Abstract Harmonic Analysis. Volume II, Structure and Analysis for Compact Groups Analysis on Locally Compact Abelian Groups
    • Springer
    • Hewitt, Edwin, Ross, Kenneth A., Abstract Harmonic Analysis. Volume II, Structure and Analysis for Compact Groups Analysis on Locally Compact Abelian Groups. 1970, Springer.
    • (1970)
    • Hewitt, E.1    Ross, K.A.2
  • 28
    • 4444338072 scopus 로고
    • Dualität lokalkompakter Gruppen
    • Springer-Verlag Berlin–Heidelberg–New York
    • Heyer, H., Dualität lokalkompakter Gruppen. 1970, Springer-Verlag, Berlin–Heidelberg–New York.
    • (1970)
    • Heyer, H.1
  • 29
    • 84972584458 scopus 로고
    • Weak Compactness and Topological Groups
    • Thesis (Ph.D.) The University of North Carolina at Chapel Hill
    • Hughes, J.R., Weak Compactness and Topological Groups. Thesis (Ph.D.), 1972, The University of North Carolina at Chapel Hill.
    • (1972)
    • Hughes, J.R.1
  • 30
    • 84972498956 scopus 로고
    • On a strong duality for separable locally compact groups
    • Ikeshoji, K., Nakagami, Y., On a strong duality for separable locally compact groups. Mem. Fac. Sci., Kyushu Univ., Ser. A 33:2 (1979), 377–389.
    • (1979) Mem. Fac. Sci., Kyushu Univ., Ser. A , vol.33 , Issue.2 , pp. 377-389
    • Ikeshoji, K.1    Nakagami, Y.2
  • 31
    • 0005825683 scopus 로고
    • Sidon Sets
    • Marcel Dekker, Inc. V New York 193 p. SFrs. 50.00
    • Lopez, Jorge M., Ross, Kenneth A., Sidon Sets. Lect. Notes Pure Appl. Math., vol. 13, 1975, Marcel Dekker, Inc. V, New York 193 p. SFrs. 50.00.
    • (1975) Lect. Notes Pure Appl. Math. , vol.13
    • Lopez, J.M.1    Ross, K.A.2
  • 32
    • 0040202798 scopus 로고
    • Unitary representations of locally compact groups. II
    • Mautner, F.I., Unitary representations of locally compact groups. II. Ann. of Math. (2) 52 (1950), 528–556.
    • (1950) Ann. of Math. (2) , vol.52 , pp. 528-556
    • Mautner, F.I.1
  • 33
    • 27844467467 scopus 로고    scopus 로고
    • Strongly mixing groups
    • Mayer, M., Strongly mixing groups. Semigroup Forum 54:3 (1997), 303–316.
    • (1997) Semigroup Forum , vol.54 , Issue.3 , pp. 303-316
    • Mayer, M.1
  • 34
    • 84966258143 scopus 로고
    • Existence of Sidon sets in discrete FC-groups
    • De Michele, Leonede, Soardi, Paolo M., Existence of Sidon sets in discrete FC-groups. Proc. Amer. Math. Soc., 55(2), mar 1976, 457.
    • (1976) Proc. Amer. Math. Soc. , vol.55 , Issue.2 , pp. 457
    • De Michele, L.1    Soardi, P.M.2
  • 35
    • 33646856307 scopus 로고
    • Lacunary sets in discrete noncommutative groups
    • Picardello, Massimo Angelo, Lacunary sets in discrete noncommutative groups. Boll. Unione Mat. Ital. (4) 8 (1973), 494–508.
    • (1973) Boll. Unione Mat. Ital. (4) , vol.8 , pp. 494-508
    • Picardello, M.A.1
  • 36
    • 0040665883 scopus 로고
    • On Pointwise and Weak Topology in Function Spaces
    • Pol, R., On Pointwise and Weak Topology in Function Spaces. 1984.
    • (1984)
    • Pol, R.1
  • 37
    • 5044235552 scopus 로고
    • A characterization of Banach spaces containing l1
    • Rosenthal, H.P., A characterization of Banach spaces containing l1. Proc. Natl. Acad. Sci. USA 71:6 (1974), 2411–2413.
    • (1974) Proc. Natl. Acad. Sci. USA , vol.71 , Issue.6 , pp. 2411-2413
    • Rosenthal, H.P.1
  • 38
    • 0010950481 scopus 로고
    • Compact Semitopological Semigroups: An Intrinsic Theory
    • Ruppert, Wolfgang, Compact Semitopological Semigroups: An Intrinsic Theory. 1984.
    • (1984)
    • Ruppert, W.1
  • 39
    • 84972521393 scopus 로고
    • Decompositions of operator algebras I and II
    • Segal, I.E., Decompositions of operator algebras I and II. Mem. Amer. Math. Soc., 9, 1951, 67.
    • (1951) Mem. Amer. Math. Soc. , vol.9 , pp. 67
    • Segal, I.E.1
  • 40
    • 84904480084 scopus 로고    scopus 로고
    • Matrix coefficients of unitary representations and associated compactifications
    • Spronk, Nico, Stokke, Ross, Matrix coefficients of unitary representations and associated compactifications. Indiana Univ. Math. J. 62:1 (2013), 99–148.
    • (2013) Indiana Univ. Math. J. , vol.62 , Issue.1 , pp. 99-148
    • Spronk, N.1    Stokke, R.2
  • 41
    • 0009430642 scopus 로고
    • Pettis Integral and Measure Theory
    • Talagrand, M., Pettis Integral and Measure Theory. 1984.
    • (1984)
    • Talagrand, M.1
  • 42
    • 0003309631 scopus 로고    scopus 로고
    • Topics in Topology
    • Todorcevic, S., Topics in Topology. 1997.
    • (1997)
    • Todorcevic, S.1
  • 43
    • 0038851918 scopus 로고    scopus 로고
    • Compact subsets of the first Baire class
    • Todorcevic, Stevo, Compact subsets of the first Baire class. J. Amer. Math. Soc. 12:4 (1999), 1179–1212.
    • (1999) J. Amer. Math. Soc. , vol.12 , Issue.4 , pp. 1179-1212
    • Todorcevic, S.1
  • 44
    • 0037658200 scopus 로고
    • Pseudocompactness on Groups
    • Ph.D Thesis Wesleyan University
    • Trigos-Arrieta, F.J., Pseudocompactness on Groups. Ph.D Thesis, 1991, Wesleyan University.
    • (1991)
    • Trigos-Arrieta, F.J.1
  • 45
    • 0002432379 scopus 로고
    • The maximal totally bounded group topology on G and the biggest minimal G-space, for abelian groups G
    • van Douwen, E.K., The maximal totally bounded group topology on G and the biggest minimal G-space, for abelian groups G. Topology Appl. 34:1 (1990), 64–91.
    • (1990) Topology Appl. , vol.34 , Issue.1 , pp. 64-91
    • van Douwen, E.K.1
  • 46
    • 84971124116 scopus 로고
    • A theorem on the continuity of homomorphisms of locally compact groups
    • Varopoulos, N.T., A theorem on the continuity of homomorphisms of locally compact groups. Proc. Cambridge Philos. Soc. 60 (1964), 449–463.
    • (1964) Proc. Cambridge Philos. Soc. , vol.60 , pp. 449-463
    • Varopoulos, N.T.1
  • 47
    • 0001363448 scopus 로고
    • On rings of operators. Reduction theory
    • von Neumann, John, On rings of operators. Reduction theory. Ann. of Math. (2) 50 (1949), 401–485.
    • (1949) Ann. of Math. (2) , vol.50 , pp. 401-485
    • von Neumann, J.1
  • 48
    • 0003967325 scopus 로고
    • L'intégration dans les groupes topologiques et ses applications
    • Weil, A., L'intégration dans les groupes topologiques et ses applications. 1965.
    • (1965)
    • Weil, A.1


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