Convex sets in Banach spaces and a problem of Rolewicz

dc.contributor.authorGranero, A. S.
dc.contributor.authorJiménez Sevilla, María del Mar
dc.contributor.authorMoreno, José Pedro
dc.description.abstractLet BX be the set of all closed, convex and bounded subsets of a Banach space X equipped with the Hausdor metric. In the rst part of this work we study the density character of BX 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).
dc.description.departmentDepto. de Análisis Matemático y Matemática Aplicada
dc.description.facultyFac. de Ciencias Matemáticas
dc.identifier.citationJ. M. Borwein and J. D. Vanderwer�, Banach spaces that admit support sets, Proc. Amer. Math. Soc. 124(3) 1996, 751-755. M. D�zamonja and K. Kunen, Properties of the class of measure separable compact spaces, Fund. Math. 147 (1995), 261-277. C. Finet and G. Godefroy, Biorthogonal systems and big quotient spaces, Contemporary Math. vol. 85 (1989), 87-110. 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. G. Godefroy, Nicely smooth Banach spaces, The University of Texas at Austin, Functional Analysis Seminar, 1984-1985 G.Godefroy, Compacts de Rosenthal, Pac. J.Math. 91(2), 1980, 293-306. B. V. Godun and S. L. Troyanski, Renorming Banach spaces with fundamental biorthogonal systems, Contemporary Math. 144 (1993), 119-126. M. Jim�enez Sevilla and J.P. Moreno, The Mazur intersection property and Asplund spaces, C.R. Acad. Sci. Paris, S�erie I, 321 (1995), 1219-1223. M. Jim�enez Sevilla and J.P. Moreno, Renorming Banach spaces with the Mazur intersection property, J. Funct. Anal. 144 (2) (1997), 486-504. M. Jim�enez Sevilla and J.P. Moreno, On denseness of certain norms in Banach spaces, Bull. Austral. Math. Soc. 54 (1996), 183-196. K. Kuratowski, Topology I, Academic Press, New York and London, 1966. D. N. Kutzarova, Convex sets containing only support points in Banach spaces with an uncountable minimal system, C. R. Acad. Bulg. Sci. 39 No. 12 (1986), 13-14. H. E. Lacey, The Isometric Theory of Classical Banach spaces, Springer-Verlag 1974. A. J. Lazar, Points of support for closed convex sets, Illinois J. Math. 25 (1981), 302{305. J. Lindenstrauss and L. Tzafriri, Classical Banach spaces II: Function spaces, Springer-Verlag, Berlin 1979. S. Mazur, � Uber schwache Konvergentz in den Raumen Lp, Studia Math. 4 (1933), 128-133. V. Montesinos, Solution to a problem of S. Rolewicz, Studia Math. 81 (1985), 65-69. S. Negrepontis, Banach spaces and Topology, Handbook of set theoretic Topology (K. Kunen and J. E. Vaughan, eds.), North-Holland, 1984, 1045-1142 A. N. Plichko, A Banach space without a fundamental biorthogonal system, Soviet. Math. Dokl. 22 (1980) No. 2, 450-453. S. Rolewicz, On convex sets containing only points of support, Comment. Math., Tomus specialis in honorem Ladislai Orlicz, I, Warszawa, 1978, 279-281. W. Schachermayer, Norm attaining operators and renormings of Banach spaces, Isr. J. Math. 44 (1983), 201-212. A. Sersouri, w-independence in non-separable Banach spaces, Contemp. Math. 85 (1989), 509-512. S. Shelah, Uncountable constructions for B. A., e.c. and Banach spaces, Isr. J. Math. 51 (1985), No. 4, 273-297.
dc.journal.titleStudia Mathematica
dc.publisherPolish Acad Sciencies Inst Mathematics
dc.relation.projectIDPB 94-0243
dc.relation.projectIDPB 93-0452
dc.rights.accessRightsrestricted access
dc.subject.unesco1201 Álgebra
dc.titleConvex sets in Banach spaces and a problem of Rolewicz
dc.typejournal article
Original bundle
Now showing 1 - 1 of 1
No Thumbnail Available
186.73 KB
Adobe Portable Document Format