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Volumn 364, Issue 12, 2012, Pages 6395-6424

Representations of dynamical systems on Banach spaces not containing L 1

Author keywords

Baire one function; Banach representation of dynamical systems; Enveloping semigroup; Fragmentability; Rosenthal's compact; Rosenthal's dichotomy; Tame system

Indexed keywords


EID: 84865267833     PISSN: 00029947     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0002-9947-2012-05549-8     Document Type: Article
Times cited : (46)

References (41)
  • 1
    • 34249658713 scopus 로고    scopus 로고
    • Almost Equicontinuity and The Enveloping Semigroup, Topological Dynamics and Applications
    • a volume in honor of R. Ellis, MR1603149 (99k:54032)
    • E. Akin, J. Auslander, and K. Berg, Almost equicontinuity and the enveloping semigroup, Topological dynamics and applications, Contemporary Mathematics 215, a volume in honor of R. Ellis, 1998, pp. 75-81. MR1603149 (99k:54032)
    • (1998) Contemporary Mathematics , vol.215 , pp. 75-81
    • Akin, E.1    Auslander, J.2    Berg, K.3
  • 2
    • 0010761868 scopus 로고
    • Pointwise compact sets in Baire-measurable functions
    • MR509077 (80b:54017)
    • J. Bourgain, D.H. Fremlin and M. Talagrand, Pointwise compact sets in Baire-measurable functions, Amer. J. of Math., 100:4 (1977), 845-886. MR509077 (80b:54017)
    • (1977) Amer. J. of Math , vol.100 , Issue.4 , pp. 845-886
    • Bourgain, J.1    Fremlin, D.H.2    Talagrand, M.3
  • 3
    • 0003222798 scopus 로고
    • Geometric Aspects of Convex Sets with the Radon-Nikodým Property
    • Springer-Verlag, MR704815 (85d:46023)
    • R.D. Bourgin, Geometric Aspects of Convex Sets with the Radon-Nikodým Property, Lecture Notes in Math. 993, Springer-Verlag, 1983. MR704815 (85d:46023)
    • (1983) Lecture Notes In Math , vol.993
    • Bourgin, R.D.1
  • 5
    • 0010897596 scopus 로고
    • Centrum voor Wiskunde en Informatica, Amsterdam, MR1002733 (90h:46037)
    • D. van Dulst, Characterization of Banach spaces not containing l1, Centrum voor Wiskunde en Informatica, Amsterdam, 1989. MR1002733 (90h:46037)
    • (1989) 1
    • van Dulst, D.1
  • 6
    • 0003934331 scopus 로고
    • W. A. Benjamin, Inc., New York, MR0267561 (42:2463)
    • R. Ellis, Lectures on Topological Dynamics, W. A. Benjamin, Inc., New York, 1969. MR0267561 (42:2463)
    • (1969) Lectures On Topological Dynamics
    • Ellis, R.1
  • 7
    • 84966218766 scopus 로고
    • Weakly almost periodic flows
    • MR930084 (89i:28010)
    • R. Ellis and M. Nerurkar, Weakly almost periodic flows, Trans. Amer. Math. Soc. 313, (1989), 103-119. MR930084 (89i:28010)
    • (1989) Trans. Amer. Math. Soc , vol.313 , pp. 103-119
    • Ellis, R.1    Nerurkar, M.2
  • 8
    • 0003798198 scopus 로고
    • General Topology
    • Heldermann Verlag, Berlin, MR1039321 (91c:54001)
    • R. Engelking, General topology, Heldermann Verlag, Berlin, 1989. MR1039321 (91c:54001)
    • (1989)
    • Engelking, R.1
  • 9
    • 0003731265 scopus 로고    scopus 로고
    • Weak Asplund spaces, Canadian Math. Soc. Series of Monographs and Advanced Texts, A Wiley-Interscience Publication, New York, MR1461271 (98h:46009)
    • M. Fabian, Gateaux differentiability of convex functions and topology. Weak Asplund spaces, Canadian Math. Soc. Series of Monographs and Advanced Texts, A Wiley-Interscience Publication, New York, 1997. MR1461271 (98h:46009)
    • (1997) Gateaux Differentiability of Convex Functions and Topology
    • Fabian, M.1
  • 10
    • 84976520098 scopus 로고    scopus 로고
    • On tame dynamical systems
    • MR2237913 (2007d:37005)
    • E. Glasner, On tame dynamical systems, Colloq. Math. 105 (2006), 283-295. MR2237913 (2007d:37005)
    • (2006) Colloq. Math , vol.105 , pp. 283-295
    • Glasner, E.1
  • 11
    • 36248970529 scopus 로고    scopus 로고
    • The structure of tame minimal dynamical systems
    • MR2371597 (2008m:37015)
    • E. Glasner, The structure of tame minimal dynamical systems, Ergod. Th. and Dynam. Sys. 27, (2007), 1819-1837. MR2371597 (2008m:37015)
    • (2007) Ergod. Th. and Dynam. Sys , vol.27 , pp. 1819-1837
    • Glasner, E.1
  • 12
    • 34249675848 scopus 로고    scopus 로고
    • Enveloping semigroups in topological dynamics
    • MR2328017 (2008f:37021)
    • E. Glasner, Enveloping semigroups in topological dynamics, Topology Appl. 154, (2007), 2344-2363. MR2328017 (2008f:37021)
    • (2007) Topology Appl , vol.154 , pp. 2344-2363
    • Glasner, E.1
  • 13
    • 34249680497 scopus 로고    scopus 로고
    • Hereditarily non-sensitive dynamical systems and linear representations
    • MR2197078 (2006m:37009)
    • E. Glasner and M. Megrelishvili, Hereditarily non-sensitive dynamical systems and linear representations, Colloq. Math., 104 (2006), no. 2, 223-283. MR2197078 (2006m:37009)
    • (2006) Colloq. Math , vol.104 , Issue.2 , pp. 223-283
    • Glasner, E.1    Megrelishvili, M.2
  • 14
    • 59349113575 scopus 로고    scopus 로고
    • New algebras of functions on topological groups arising from G-spaces
    • MR2439022 (2010f:37015)
    • E. Glasner and M. Megrelishvili, New algebras of functions on topological groups arising from G-spaces, Fundamenta Math., 201 (2008), 1-51. MR2439022 (2010f:37015)
    • (2008) Fundamenta Math , vol.201 , pp. 1-51
    • Glasner, E.1    Megrelishvili, M.2
  • 16
    • 58449115114 scopus 로고    scopus 로고
    • On metrizable enveloping semigroups
    • MR2391152 (2009a:37013)
    • E. Glasner, M. Megrelishvili and V.V. Uspenskij, On metrizable enveloping semigroups, Israel J. of Math. 164 (2008), 317-332. MR2391152 (2009a:37013)
    • (2008) Israel J. of Math , vol.164 , pp. 317-332
    • Glasner, E.1    Megrelishvili, M.2    Uspenskij, V.V.3
  • 17
    • 0001138434 scopus 로고
    • Sensitive dependence on initial conditions
    • MR1251259 (94j:58109)
    • E. Glasner and B. Weiss, Sensitive dependence on initial conditions, Nonlinearity 6, (1993), 1067-1075. MR1251259 (94j:58109)
    • (1993) Nonlinearity , vol.6 , pp. 1067-1075
    • Glasner, E.1    Weiss, B.2
  • 18
    • 84972541739 scopus 로고
    • Compacts de Rosenthal
    • MR615679 (82f:54030)
    • G. Godefroy, Compacts de Rosenthal, Pacific J. Math., 91 (1980), 293-306. MR615679 (82f:54030)
    • (1980) Pacific J. Math , vol.91 , pp. 293-306
    • Godefroy, G.1
  • 20
    • 33749337883 scopus 로고    scopus 로고
    • Tame systems and scrambled pairs under an abelian group action
    • MR2266373 (2007j:37012)
    • W. Huang, Tame systems and scrambled pairs under an abelian group action, Ergod. Th. Dynam. Sys. 26 (2006), 1549-1567. MR2266373 (2007j:37012)
    • (2006) Ergod. Th. Dynam. Sys , vol.26 , pp. 1549-1567
    • Huang, W.1
  • 21
    • 84966204570 scopus 로고
    • A separable somewhat reflexive Banach space with nonseparable dual
    • MR0417763 (54:5811)
    • R.C. James, A separable somewhat reflexive Banach space with nonseparable dual, Bull. Amer. Math. Soc., 80 (1974), 738-743. MR0417763 (54:5811)
    • (1974) Bull. Amer. Math. Soc , vol.80 , pp. 738-743
    • James, R.C.1
  • 22
    • 0008979727 scopus 로고
    • Σ-fragmentability of multivalued maps and selection theorems
    • MR1244937 (94m:46023)
    • J.E. Jayne, J. Orihuela, A.J. Pallares and G. Vera, σ-fragmentability of multivalued maps and selection theorems, J. Funct. Anal. 117 (1993), no. 2, 243-273. MR1244937 (94m:46023)
    • (1993) J. Funct. Anal , vol.117 , Issue.2 , pp. 243-273
    • Jayne, J.E.1    Orihuela, J.2    Pallares, A.J.3    Vera, G.4
  • 23
    • 0001843630 scopus 로고
    • Borel selectors for upper semicontinuous set-valued maps
    • MR793237 (87a:28011)
    • J.E. Jayne and C.A. Rogers, Borel selectors for upper semicontinuous set-valued maps, Acta Math. 155 (1985), 41-79. MR793237 (87a:28011)
    • (1985) Acta Math , vol.155 , pp. 41-79
    • Jayne, J.E.1    Rogers, C.A.2
  • 24
    • 0003589707 scopus 로고
    • Classical Descriptive Set Theory
    • Springer-Verlag, MR1321597 (96e:03057)
    • A.S. Kechris, Classical descriptive set theory, Graduate Texts in Mathematics, 156, Springer-Verlag, 1991. MR1321597 (96e:03057)
    • (1991) Graduate Texts In Mathematics , vol.156
    • Kechris, A.S.1
  • 25
    • 34347347064 scopus 로고    scopus 로고
    • *-dynamics
    • MR2317754 (2009a:46126)
    • *-dynamics, Math. Ann. 338 (2007), 869-926. MR2317754 (2009a:46126)
    • (2007) Math. Ann , vol.338 , pp. 869-926
    • Kerr, D.1    Li, H.2
  • 26
    • 27744551492 scopus 로고
    • Enveloping semigrops for flows
    • MR1660377 (99i:47056)
    • A. Köhler, Enveloping semigrops for flows, Proceedings of the Royal Irish Academy, 95A (1995), 179-191. MR1660377 (99i:47056)
    • (1995) Proceedings of the Royal Irish Academy , vol.95 A , pp. 179-191
    • Köhler, A.1
  • 27
    • 0003103708 scopus 로고
    • Examples of separable spaces which do not contain l1 and whose duals are nonseparable
    • MR0390720 (52:11543)
    • J. Lindenstrauss and C. Stegall, Examples of separable spaces which do not contain l1 and whose duals are nonseparable, Studia Math., 54 (1975), 81-105. MR0390720 (52:11543)
    • (1975) Studia Math , vol.54 , pp. 81-105
    • Lindenstrauss, J.1    Stegall, C.2
  • 28
    • 1842598881 scopus 로고    scopus 로고
    • Fragmentability and continuity of semigroup actions
    • MR1621881 (99c:54053)
    • M. Megrelishvili, Fragmentability and continuity of semigroup actions, Semigroup Forum, 57 (1998), 101-126. MR1621881 (99c:54053)
    • (1998) Semigroup Forum , vol.57 , pp. 101-126
    • Megrelishvili, M.1
  • 29
    • 0012894741 scopus 로고    scopus 로고
    • Operator topologies and reflexive representability
    • Heldermann Verlag, Berlin, MR1858149 (2002m:46027)
    • M. Megrelishvili, Operator topologies and reflexive representability, In: "Nuclear groups and Lie groups" Research and Exposition in Math. series, vol. 24, Heldermann Verlag, Berlin, 2001, 197-208. MR1858149 (2002m:46027)
    • (2001) Nuclear Groups and Lie Groups Research and Exposition In Math. Series , vol.24 , pp. 197-208
    • Megrelishvili, M.1
  • 30
    • 34249670447 scopus 로고    scopus 로고
    • Fragmentability and representations of flows
    • MR2077804 (2005h:37042)
    • M. Megrelishvili, Fragmentability and representations of flows, Topology Proceedings, 27:2 (2003), 497-544. See also: www.math.biu.ac.il/megereli. MR2077804 (2005h:37042)
    • (2003) Topology Proceedings , vol.27 , Issue.2 , pp. 497-544
    • Megrelishvili, M.1
  • 32
    • 84972579811 scopus 로고
    • Separate continuity and joint continuity
    • MR0370466 (51:6693)
    • I. Namioka, Separate continuity and joint continuity, Pacific. J. Math., 51 (1974), 515-531. MR0370466 (51:6693)
    • (1974) Pacific. J. Math , vol.51 , pp. 515-531
    • Namioka, I.1
  • 33
    • 84976003905 scopus 로고
    • Radon-Nikodým compact spaces and fragmentability
    • MR933504 (89i:46021)
    • I. Namioka, Radon-Nikodým compact spaces and fragmentability, Mathematika 34, (1987), 258-281. MR933504 (89i:46021)
    • (1987) Mathematika , vol.34 , pp. 258-281
    • Namioka, I.1
  • 34
    • 84972577815 scopus 로고
    • Banach spaces which are Asplund spaces
    • MR0390721 (52:11544)
    • I. Namioka and R.R. Phelps, Banach spaces which are Asplund spaces, Duke Math. J., 42 (1975), 735-750. MR0390721 (52:11544)
    • (1975) Duke Math. J , vol.42 , pp. 735-750
    • Namioka, I.1    Phelps, R.R.2
  • 35
    • 51249189706 scopus 로고
    • A double-dual characterization of separable Banach spaces containing l1
    • MR0377482 (51:13654)
    • E. Odell and H. P. Rosenthal, A double-dual characterization of separable Banach spaces containing l1, Israel J. Math., 20 (1975), 375-384. MR0377482 (51:13654)
    • (1975) Israel J. Math , vol.20 , pp. 375-384
    • Odell, E.1    Rosenthal, H.P.2
  • 36
    • 84968483704 scopus 로고
    • Note on Compact Sets of First Baire Class Functions
    • MR813828 (87b:54033)
    • R. Pol, Note on Compact Sets of First Baire Class Functions, Proc. Amer. Math. Soc. 96, No. 1. (1986), pp. 152-154. MR813828 (87b:54033)
    • (1986) Proc. Amer. Math. Soc , vol.96 , Issue.1 , pp. 152-154
    • Pol, R.1
  • 37
    • 0013549509 scopus 로고
    • Sets with the weak Radon-Nikodým property in dual Banach spaces
    • MR703283 (84h:46028)
    • L.H. Riddle, E. Saab and J.J. Uhl, Sets with the weak Radon-Nikodým property in dual Banach spaces, Indiana Univ. Math. J., 32 (1983), 527-541. MR703283 (84h:46028)
    • (1983) Indiana Univ. Math. J. , vol.32 , pp. 527-541
    • Riddle, L.H.1    Saab, E.2    Uhl, J.J.3
  • 38
    • 5044235552 scopus 로고
    • A characterization of Banach spaces containing l1
    • MR0358307 (50:10773)
    • H.P. Rosenthal, A characterization of Banach spaces containing l1, Proc. Nat. Acad. Sci. U.S.A., 71 (1974), 2411-2413. MR0358307 (50:10773)
    • (1974) Proc. Nat. Acad. Sci. U.S.A , vol.71 , pp. 2411-2413
    • Rosenthal, H.P.1
  • 39
    • 0011602812 scopus 로고
    • Point-wise compact subsets of the first Baire class
    • MR0438113 (55:11032)
    • H.P. Rosenthal, Point-wise compact subsets of the first Baire class, Amer. J. of Math., 99:2 (1977), 362-378. MR0438113 (55:11032)
    • (1977) Amer. J. of Math , vol.99 , Issue.2 , pp. 362-378
    • Rosenthal, H.P.1
  • 40
    • 84966250081 scopus 로고
    • Some recent discoveries in the isomorphic theory of Banach spaces
    • MR499730 (80d:46023)
    • H.P. Rosenthal, Some recent discoveries in the isomorphic theory of Banach spaces, Bull. Amer. Math. Soc. 84:5 (1978), 803-831. MR499730 (80d:46023)
    • (1978) Bull. Amer. Math. Soc , vol.84 , Issue.5 , pp. 803-831
    • Rosenthal, H.P.1
  • 41
    • 84972565104 scopus 로고
    • A dual geometric characterization of Banach spaces not containing l1
    • MR691612 (85c:46013)
    • E. Saab and P. Saab, A dual geometric characterization of Banach spaces not containing l1, Pacific J. Math., 105:2 (1983), 413-425. MR691612 (85c:46013)
    • (1983) Pacific. J. Math , vol.105 , Issue.2 , pp. 413-425
    • Saab, E.1    Saab, P.2


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