Hostname: page-component-586b7cd67f-gb8f7 Total loading time: 0 Render date: 2024-11-28T06:26:42.719Z Has data issue: false hasContentIssue false
  • English
  • Français

Borel and analytic sets in Banach spaces

Part of: Normed linear spaces and Banach spaces; Banach lattices

Published online by Cambridge University Press:  26 February 2010

Robert Kaufman
Robert Kaufman
Affiliation:
Department of Mathematics, University of Illinois, 273 Altgeld Hall, MC-382, 1409, West Green Street, Urbana, IL 61801, U.S.A.
Get access

Extract

We prove theorems relating descriptive set theory to nonreflexive Banach spaces. In Theorems 1, 2, and 3 X denotes a Banach space that is separable, but is not reflexive. JX denotes the cannonical embedding of X in X**.

MSC classification

Secondary: 46B20: Geometry and structure of normed linear spaces
Type
Research Article
Information
Mathematika , Volume 41 , Issue 1 , June 1994 , pp. 133 - 140
Copyright
Copyright © University College London 1994

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

C.Becker, H.. Pointwise limits of sequences and ∑12 sets. Fund. Math., 128 (1987), 159–169.CrossRefGoogle Scholar
2.Casazza, P. G. and Lohman, R. H.. A general construction of the type of R. C. James. Canadian J. Math 27 (1975), 1263–1270.Google Scholar
3.Day, M. M.. Ergeb der Math, n.s., 3rd Ed., vol. 21 (Springer-Verlag, 1973).Google Scholar
4.Dunford, N. and Schwartz, J. T.. Linear Operators I, (Interscience, New York, 1958).Google Scholar
5.James, R. C.. A non-reflexive Banach space isometric with its second conjugate space. Proc. Nat. Acad. Sci. (USA), 37 (1951), 174–177.CrossRefGoogle ScholarPubMed
6.Jayne, J. E. and Rogers, C. A.. The extremal structure of convex sets. J. Fund. Anal., 26 (1977), 251–288.CrossRefGoogle Scholar
7.Kaufman, R.. Topics on analytic sets. Fund. Math., 139 (1991), 215–229.CrossRefGoogle Scholar
8.Lindenstrauss, J.. On James' paper “pseparable conjugate spaces”. Israel J. Math., 9 (1971), 279–284.CrossRefGoogle Scholar
9.Pelczyriski, A.. A note on the paper of I. Singer “Basic sequence and reflexivity of Banach spaces”. Studio Math., 21 (1962), 371–374.Google Scholar