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Isometries of non-commutative Lp-spaces

Published online by Cambridge University Press:  24 October 2008

F. J. Yeadon
F. J. Yeadon
Affiliation:
University of Hull
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Extract

The spaces Lp(, φ) for 1 ≤ p ≤ ∞, where φ is a faithful semifinite normal trace on a von Neumann algebra , are defined in (10),(2),(14). The problem of determining the general form of an isometry of one such space into another has been studied in (i), (6), (9), (12), (5). Our main result, Theorem 2, is a characterization of such isometries for 1 ≤ p ≤ ∞, ≠ 2. The method of proof is based on that of (7), where isometries between Lp function spaces are characterized. The main step in the proof is Theorem 1, which gives the conditions under which equality holds in Clarkson's inequality.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 90 , Issue 1 , July 1981 , pp. 41 - 50
Copyright
Copyright © Cambridge Philosophical Society 1981

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References

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