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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

A representation theorem for $ L^{p}$ spaces


Author: Marek Kanter
Journal: Proc. Amer. Math. Soc. 31 (1972), 472-474
MSC: Primary 46.35
DOI: https://doi.org/10.1090/S0002-9939-1972-0290088-6
MathSciNet review: 0290088
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Abstract: Using the theory of symmetric stable process of index $ p \in (0,2]$, we prove that if a sepaéable Frechet space $ L$ has all its finite dimensional subspaces linearly isometric with a subspace of $ {L^p}[0,1]$ then $ L$ itself is linearly isometric with a subspace of $ {L^p}[0,1]$.


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DOI: https://doi.org/10.1090/S0002-9939-1972-0290088-6
Keywords: Linear isometry, symmetric stable process, weak convergence of measures
Article copyright: © Copyright 1972 American Mathematical Society