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1998 | 129 | 1 | 19-29
Tytuł artykułu

Convex sets in Banach spaces and a problem of Rolewicz

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
Let $B_x$ be the set of all closed, convex and bounded subsets of a Banach space X equipped with the Hausdorff metric. In the first part of this work we study the density character of $B_x$ and investigate its connections with the geometry of the space, in particular with a property shared by the spaces of Shelah and Kunen. In the second part we are concerned with the problem of Rolewicz, namely the existence of support sets, for the case of spaces C(K).
Słowa kluczowe
Czasopismo
Rocznik
Tom
129
Numer
1
Strony
19-29
Opis fizyczny
Daty
wydano
1998
otrzymano
1996-09-23
poprawiono
1997-11-07
Twórcy
  • Departamento de Análisis Matemático, Facultad de Ciencias Matemáticas, Universidad Complutense de Madrid, 28040 Madrid, Spain., granero@eucmax.sim.ucm.es
  • Departamento de Análisis Matemático, Facultad de Ciencias Matemáticas, Universidad Complutense de Madrid, 28040 Madrid, Spain., marjim@sunam1.mat.ucm.es
autor
Bibliografia
  • [1] J. M. Borwein and J. D. Vanderwerff, Banach spaces that admit support sets, Proc. Amer. Math. Soc. 124 (1996), 751-755.
  • [2] M. Džamonja and K. Kunen, Properties of the class of measure separable compact spaces, Fund. Math. 147 (1995), 261-277.
  • [3] C. Finet and G. Godefroy, Biorthogonal systems and big quotient spaces, in: Contemp. Math. 85, Amer. Math. Soc., 1989, 87-110.
  • [4] J. R. Giles, D. A. Gregory and B. Sims, Characterization of normed linear spaces with Mazur's intersection property, Bull. Austral. Math. Soc. 18 (1978), 471-476.
  • [5] G. Godefroy, Nicely smooth Banach spaces, in: Functional Analysis Seminar, The University of Texas at Austin, 1984-1985.
  • [6] G. Godefroy, Compacts de Rosenthal, Pacific J. Math. 91 (1980), 293-306.
  • [7] B. V. Godun and S. L. Troyanski, Renorming Banach spaces with fundamental biorthogonal systems, in: Contemp. Math. 144, Amer. Math. Soc., 1993, 119-126.
  • [8] M. Jiménez Sevilla and J. P. Moreno, The Mazur intersection property and Asplund spaces, C. R. Acad. Sci. Paris Sér. I 321 (1995), 1219-1223.
  • [9] M. Jiménez Sevilla and J. P. Moreno, Renorming Banach spaces with the Mazur intersection property, J. Funct. Anal. 144 (1997), 486-504.
  • [10] M. Jiménez Sevilla and J. P. Moreno, On denseness of certain norms in Banach spaces, Bull. Austral. Math. Soc. 54 (1996), 183-196.
  • [11] K. Kuratowski, Topology I, Academic Press, New York and London, 1966.
  • [12] D. N. Kutzarova, Convex sets containing only support points in Banach spaces with an uncountable minimal system, C. R. Acad. Bulg. Sci. 39 (12) (1986), 13-14.
  • [13] H. E. Lacey, The Isometric Theory of Classical Banach spaces, Springer, 1974.
  • [14] A. J. Lazar, Points of support for closed convex sets, Illinois J. Math. 25 (1981), 302-305.
  • [15] J. Lindenstrauss and L. Tzafriri, Classical Banach Spaces II: Function Spaces, Springer, Berlin, 1979.
  • [16] S. Mazur, Über schwache Konvergenz in den Räumen $L^p$, Studia Math. 4 (1933), 128-133.
  • [17] V. Montesinos, Solution to a problem of S. Rolewicz, ibid. 81 (1985), 65-69.
  • [18] S. Negrepontis, Banach spaces and topology, in: Handbook of Set-Theoretic Topology, K. Kunen and J. E. Vaughan (eds.), North-Holland, 1984, 1045-1142.
  • [19] A. N. Plichko, A Banach space without a fundamental biorthogonal system, Soviet Math. Dokl. 22 (1980), 450-453.
  • [20] S. Rolewicz, On convex sets containing only points of support, Comment. Math., Tomus specialis in honorem Ladislai Orlicz, I, 1978, 279-281.
  • [21] W. Schachermayer, Norm attaining operators and renormings of Banach spaces, Israel J. Math. 44 (1983), 201-212.
  • [22] A. Sersouri, w-independence in non-separable Banach spaces, in: Contemp. Math. 85, Amer. Math. Soc., 1989, 509-512.
  • [23] S. Shelah, Uncountable constructions for B. A., e.c. and Banach spaces, Israel J. Math. 51 (1985), 273-297.
Typ dokumentu
Bibliografia
Identyfikatory
Identyfikator YADDA
bwmeta1.element.bwnjournal-article-smv129i1p19bwm
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