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Tytuł artykułu

Kadec norms and Borel sets in a Banach space

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Abstrakty
EN
We introduce a property for a couple of topologies that allows us to give simple proofs of some classic results about Borel sets in Banach spaces by Edgar, Schachermayer and Talagrand as well as some new results. We characterize the existence of Kadec type renormings in the spirit of the new results for LUR spaces by Moltó, Orihuela and Troyanski.
Twórcy
autor
  • Mathématiques Pures, Université Bordeaux 1, 351, cours de la Libération, 33405 Talence Cedex, France , raja@math.u-bordeaux.fr
Bibliografia
  • [1] G. A. Alexandrov, One generalization of the Kadec property, preprint, 1993.
  • [2] C. Bessaga and A. Pełczyński, Selected Topics in Infinite-Dimensional Topology, Monografie Mat. 58, PWN-Polish Sci. Publ., Warszawa, 1975.
  • [3] B. Cascales and G. Vera, Topologies weaker than the weak topology of a Banach space, J. Math. Anal. Appl. 182 (1994), 41-68.
  • [4] R. Deville, G. Godefroy and V. Zizler, Smoothness and Renormings in Banach Spaces, Pitman Monographs Surveys 64, Longman Sci. Tech., 1993.
  • [5] G. A. Edgar, Measurability in a Banach space, Indiana Univ. Math. J. 26 (1977), 663-677.
  • [6] G. A. Edgar, Measurability in a Banach space II, ibid. 28 (1979), 559-579.
  • [7] G. A. Edgar, A long James space, in: Measure Theory (Oberwolfach 1979), Lecture Notes in Math. 794, Springer, 1980, 31-37.
  • [8] M. Fabian, On a dual locally uniformly rotund norm on a dual Vašák space, Studia Math. 101 (1991), 69-81.
  • [9] M. Fabian and G. Godefroy, The dual of every Asplund space admits a projectional resolution of the identity, ibid. 91 (1988), 141-151.
  • [10] R. W. Hansell, Descriptive sets and the topology of nonseparable Banach spaces, preprint.
  • [11] R. Haydon, Trees in renorming theory, preprint.
  • [12] R. Haydon, Baire trees, bad norms and the Namioka property, preprint.
  • [13] R. Haydon, J. E. Jayne, I. Namioka and C. A. Rogers, Continuous functions on totally ordered spaces that are compact in their order topologies, preprint.
  • [14] J. E. Jayne, I. Namioka and C. A. Rogers, Norm fragmented weak* compact sets, Collect. Mat. 41 (1990), 133-163.
  • [15] J. E. Jayne, I. Namioka and C. A. Rogers, σ-fragmentable Banach spaces, Mathematika 39 (1992), 161-188 and 197-215.
  • [16] J. E. Jayne, I. Namioka and C. A. Rogers, Topological properties of Banach spaces, Proc. London Math. Soc. (3) 66 (1993), 651-672.
  • [17] J. E. Jayne, I. Namioka and C. A. Rogers, Continuous functions on products of compact Hausdorff spaces, to appear.
  • [18] G. Lancien, Théorie de l'indice et problèmes de renormage en géométrie des espaces de Banach, thèse, Paris, 1992.
  • [19] A. Moltó, J. Orihuela and S. Troyanski, Locally uniform rotund renorming and fragmentability, Proc. London Math. Soc. (3) 75 (1997), 619-640.
  • [20] A. Moltó, J. Orihuela, S. Troyanski and M. Valdivia, On weakly locally uniformly rotund Banach spaces, to appear.
  • [21] I. Namioka, Radon-Nikodym compact spaces and fragmentability, Mathematika 34 (1989), 258-281.
  • [22] L. Oncina, Borel sets and σ-fragmentability of a Banach space, Master Degree Thesis at University College London, 1996.
  • [23] M. Raja, On topology and renorming of a Banach space, C. R. Acad. Bulgare Sci., to appear.
  • [24] M. Talagrand, Sur une conjecture de H. H. Corson, Bull. Sci. Math. 99 (1975), 211-212.
  • [25] M. Talagrand, Sur la structure borélienne des espaces analytiques, ibid. 101 (1977), 415-422.
  • [26] M. Talagrand, Comparaison des boréliens d'un espace de Banach pour les topologies fortes et faibles, Indiana Univ. Math. J. 27 (1978), 1001-1004.
  • [27] M. Valdivia, Projective resolutions of identity in C(K) spaces, Arch. Math. (Basel) 54 (1990), 493-498.
  • [28] L. Vašák, On one generalization of weakly compactly generated spaces, Studia Math. 70 (1981), 11-19.
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-smv136i1p1bwm
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