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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

1. Dixmier, J., Les algebres d'operateurs dans l'espace Hilbertien (Gauthier Villars, Paris, 1969).Google Scholar
2. Forelli, F., The isometries of H*, Can. J. Math. 16 (1964), 721–728.Google Scholar
3. Dixmier, J., Formes linéaires sur un anneau d'operateurs, Bull. Soc. Math. France 81 (1953), 9–39.Google Scholar
4. Kadison, R. V., Isometries of operator algebras, Annals of Math. 54 (1951), 325–338.Google Scholar
5. Kunze, R. A., Lp Fourier transforms on locally compact unimodular groups, Trans. Amer. Math. Soc. 89 (1958), 519–540.Google Scholar
6. Nelson, E., Notes on non-commutative integration, J. Funct. Anal. 15 (1974), 103–116.Google Scholar
7. Schneider, R., Unit preserving isometries are homomorphisms in certain Lp, Can. J. Math. 28 (1975), 133–137.Google Scholar
8. Segal, I. E., A non-commutative extension of abstract integration, Annals of Math. 57 (1953), 401–457.Google Scholar
9. Broise, M., Sur les isomorphismes de certaines algebres de Von Neumann, Ann. Sci. Ec. Norm. Sup. 83, 3eme série (1966), 91–111.Google Scholar
10. Russo, B., Isometries of Lp spaces associated with finite Von Neumann algebras, Bull. Am. Math. Soc. 74 (1968), 228–232.Google Scholar
11. StOrmer, E., On the Jordan structure of C* algebras, Trans. Amer. Math. Soc. 120 (1965), 438–447.Google Scholar
12. Young, R. M. G., Some unital isometries on *'algebras, Preprint.Google Scholar