Hostname: page-component-cd9895bd7-dzt6s Total loading time: 0 Render date: 2024-12-24T17:30:03.949Z Has data issue: false hasContentIssue false
  • English
  • Français

Isometric Stability Property of Certain Banach Spaces

Published online by Cambridge University Press:  20 November 2018

Alexander Koldobsky
Alexander Koldobsky*
Affiliation:
Division of Mathematics, Computer Science and Statistics, University of Texas at San Antonio, San Antonio, Texas 78249 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 one of the spaces C(K) and L1, F be an arbitrary Banach space, p > 1, and (X, σ) be a space with a finite measure. We prove that E is isometric to a subspace of the Lebesgue-Bochner space LP(X; F) only if E is isometric to a subspace of F. Moreover, every isometry T from E into Lp(X; F) has the form Te(x) = h(x)U(x)e, e ∊ E, where h: X —> R is a measurable function and, for every x ∊ X, U(x) is an isometry from E to F

Keywords

46B0447B80isometriesLebesgue-Bochner spacesrandom operators
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 38 , Issue 1 , 01 March 1995 , pp. 93 - 97
Copyright
Copyright © Canadian Mathematical Society 1995

References

1. Bourgain, J., An averaging result for c0-sequences, Bull. Soc. Math. Belg. Sér. B 30(1978), 83–87.Google Scholar
2. Dowling, P. N., A stability property of a class of Banach spaces not containing c$, Canad. Math. Bull. 35(1992), 56–60.Google Scholar
3. Emmanuele, G., Copies of l∞ in Köthe spaces of vector valued functions, Illinois J. Math. 36(1992), 293– 296.Google Scholar
4. Koldobsky, A., Isometries of Lp(X;Lq) and equimeasurability', Indiana Univ. Math. J. 40(1991), 677–705.Google Scholar
5. Koldobsky, A., Measures on spaces of operators and isometries, J. Soviet Math. 42(1988), 1628–1636.Google Scholar
6. Kwapien, S., On Banach spaces containing CQ, Studia Math. 52(1974), 187–188.Google Scholar
7. Mendoza, J., Copies of l∞ in Lp(μ;X), Proc. Amer. Math. Soc. 109(1990), 125–127.Google Scholar
8. Pisier, G., Une propriété de stabilité de la classe des espaces ne contenant pas l1 , Acad, C. R.. Sci. Paris Sér. A 86(1978), 747–749.Google Scholar
9. Raynaud, Y., Sous espaces lr et géométrie des espaces LP(Lq) et Lϕ , Acad, C. R.. Sci. Paris Sér. I Math. 301(1985), 299–302.Google Scholar
10. Saab, E. and Saab, P., On stability problems of some properties in Banach spaces, Function spaces (ed. Jarosz, K.), Lecture Notes in Pure and Appl. Math. 136(1992), 367–394.Google Scholar