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1994 | 111 | 1 | 69-80
Tytuł artykułu

σ-fragmented Banach spaces II

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Recent papers have investigated the properties of σ-fragmented Banach spaces and have sought to find which Banach spaces are σ-fragmented and which are not. Banach spaces that have a norming M-basis are shown to be σ-fragmented using weakly closed sets. Zizler has shown that Banach spaces satisfying certain conditions have locally uniformly convex norms. Banach spaces that satisfy similar, but weaker conditions are shown to be σ-fragmented. An example, due to R. Pol, is given of a Banach space that is σ-fragmented using differences of weakly closed sets, but is not σ-fragmented using weakly closed sets.
Słowa kluczowe
Kategorie tematyczne
Czasopismo
Rocznik
Tom
111
Numer
1
Strony
69-80
Opis fizyczny
Daty
wydano
1994
otrzymano
1993-10-21
Twórcy
autor
  • Department of Mathematics, University College London, Gower Street, London WC1E 6BT, England
autor
  • Department of Mathematics, GN-50, University of Washington, Seattle, Washington 98195, U.S.A.
autor
  • Department of Mathematics, University College London, Gower Street, London WC1E 6BT, England
Bibliografia
  • [1] D. Amir and J. Lindenstrauss, The structure of weakly compact sets in Banach spaces, Ann. of Math. 88 (1968), 35-46.
  • [2] R. Deville, Problèmes de renormages, J. Funct. Anal. 68 (1986), 117-129.
  • [3] R. Deville, G. Godefroy and V. Zizler, Smoothness and Renormings in Banach Spaces, Pitman Monographs Math. 64, Longman, Essex, 1993.
  • [4] R. Haydon, Some problems about scattered spaces, Séminaire Initiation à l'Analyse 9 (1989/90), 1-10.
  • [5] R. Haydon, Trees in renorming theory, preprint.
  • [6] R. Haydon and C. A. Rogers, A locally uniformly convex renorming for certain C(K), Mathematika 37 (1990), 1-8.
  • [7] J. E. Jayne, I. Namioka and C. A. Rogers, Norm fragmented weak compact sets, Collect. Math. 41 (1990), 133-163.
  • [8] J. E. Jayne, I. Namioka and C. A. Rogers, σ-fragmented Banach spaces, Mathematika 39 (1992), 161-188 and 197-215.
  • [9] J. E. Jayne, I. Namioka and C. A. Rogers, Topological properties of Banach spaces, Proc. London Math. Soc. 66 (1993), 651-672.
  • [10] J. E. Jayne, I. Namioka and C. A. Rogers, Fragmentability and σ-fragmentability, Fund. Math. 143 (1993), 207-220.
  • [11] J. E. Jayne, I. Namioka and C. A. Rogers, Continuous functions on compact totally ordered spaces, J. Funct. Anal., to appear.
  • [12] J. E. Jayne, J. Orihuela, A. J. Pallarés and G. Vera, σ-fragmentability of multivalued maps and selection theorems, J. Funct. Anal. 117 (1993), 243-373.
  • [13] K. John and V. Zizler, Smoothness and its equivalents in weakly compactly generated Banach spaces, ibid. 15 (1974), 1-11.
  • [14] K. John and V. Zizler, Some remarks on non-separable Banach spaces with Markuševič basis, Comment. Math. Univ. Carolin. 15 (1974), 679-691.
  • [15] I. Namioka, Radon-Nikodým compact spaces and fragmentability, Mathematika 34 (1987), 258-281.
  • [16] I. Namioka and R. Pol, Mappings of Baire spaces into function spaces and Kadec renorming, Israel J. Math. 78 (1992), 1-20.
  • [17] N. K. Ribarska, Internal characterization of fragmentable spaces, Mathematika 34 (1987), 243-257.
  • [18] I. Singer, Bases in Banach Spaces II, Springer, Berlin, 1981.
  • [19] V. Zizler, Locally uniformly rotund renorming and decomposition of Banach spaces, Bull. Austral. Math. Soc. 29 (1984), 259-265.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-smv111i1p69bwm
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