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Hilbert spaces have the Banach-Stone property for Bochner spaces

Published online by Cambridge University Press:  17 April 2009

Peter Greim
Peter Greim
Affiliation:
Mathematisches Institut, Freie Universität, Arnimallee 2–6, D 1000 Berlin 33, Germany.
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Abstract

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Let (ωi, σi, μi.) be two positive finite measure spaces, V a non-zero Hilbert space, and 1 ≤ p < ∞, p # 2. In this article it is shown that each surjective linear isometry between the Bochner spaces induces a Boolean isomorphism between the measure algebras , thus generalizing a result of Cambern's for separable Hilbert spaces.

This Banach–Stone type theorem is achieved via a description of the Lp-structure of .

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 27 , Issue 1 , February 1983 , pp. 121 - 128
Copyright
Copyright © Australian Mathematical Society 1983

References

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