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Isometric Mappings of Non-Commutative LP Spaces

Published online by Cambridge University Press:  20 November 2018

A. Katavolos
A. Katavolos*
Affiliation:
Bedford College, University of London, London, England
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If the Lp spaces of two measure spaces are “the same”, to what extent can we identify the underlying measure spaces? This question has been partially answered by Schneider [7] (extending results of Forelli [2]). He proves that a linear isometry between the Lv spaces of two finite measure spaces is in fact an (isometric) homomorphism between the corresponding L∞ spaces, if it preserves the identity.

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 28 , Issue 6 , 01 December 1976 , pp. 1180 - 1186
Copyright
Copyright © Canadian Mathematical Society 1976

References

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