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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.
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Abstract

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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

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