Hostname: page-component-78c5997874-xbtfd Total loading time: 0 Render date: 2024-11-10T15:10:07.515Z Has data issue: false hasContentIssue false
  • English
  • Français

A Stability Property of a Class of Banach Spaces Not Containing c0

Published online by Cambridge University Press:  20 November 2018

Patrick N. Dowling
Patrick N. Dowling*
Affiliation:
Department of Mathematics and Statistics Miami University Oxford, Ohio 45056 U.S.A.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

Let E be a Banach ideal space and X be a Banach space. The Banach function space E(X) does not contain a copy of C0 if and only if neither E nor X contains a copy of c0. Some extensions of this result are also noted.

Keywords

46E4043A46.
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 35 , Issue 1 , 01 March 1992 , pp. 56 - 60
Copyright
Copyright © Canadian Mathematical Society 1992

References

1. Bukhvalov, A. V., Radon-Nikodymproperty in Banach spaces of measurable vector-functions, Mat. Zametki 26(1979),975–884. English translation: Math. Notes 26(1979),939–944.Google Scholar
2. Bukhvalov, A. V., Geometric Properties of Banach spaces of measurable vector-valued functions, Soviet Math. Dokl., (2) 19(1978),501–505.Google Scholar
3. Bukhvalov, A. V., On the analytic Radon-Nikodymproperty, preprint.Google Scholar
4. Bukhvalov, A. V. and Danielvich, A. A., Boundary properties of analytic and harmonic functions with values in a Banach space, Mat. Zematki. 31(1982),203–214; English translation: Math. Notes 31(1982),104–110.Google Scholar
5. Dowling, P. N., Duality in some vector-valued function spaces, Rocky Mountain J. Math., to appear.Google Scholar
6. Dowling, P. N., Radon-Nikodym properties associated with subsets of countable discrete abelian groups, Trans. Amer. Math. Soc., 327(1991),879–890.Google Scholar
7. Edgar, G. A., Banach spaces with the analytic Radon-Nikodym property and compact abelian groups, Almost Everywhere Convergence, Academic Press Inc., Boston, MA (1989), 195–213.Google Scholar
8. Kwapien, S., On Banach spaces containing c0 , Studia Math. 52(1974),187–188.Google Scholar
9. Lindenstrauss, J. and Tzafriri, L., Classical Banach spaces II. Function Spaces, Ergebnisse der Mathematik und ihrer Grenzgebiete, 92(1979). Berlin-Heidelberg-New York: Springer-Verlag.Google Scholar
10. Rudin, W., Fourier analysis on groups, Tracts in Mathematics, 12(1962).Google Scholar