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Proceedings of the American Mathematical Society

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Remarks on dilations in $ L\sb{p}$-spaces


Authors: M. A. Akcoglu and L. Sucheston
Journal: Proc. Amer. Math. Soc. 53 (1975), 80-82
MSC: Primary 47A35; Secondary 28A65
DOI: https://doi.org/10.1090/S0002-9939-1975-0377558-X
MathSciNet review: 0377558
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Abstract: Let $ (X,\;\mathcal{F},\;\mu )$ be a nonatomic measure space. It is shown that there exists a unitary operator $ U$ on $ {L_2} = {L_2}(X,\;\mathcal{F},\;\mu )$, a function $ f\epsilon {L_2}$, and a nonnull set $ A$ in $ \mathcal{F}$ such that $ {n^{ - 1}}\Sigma _{i = 1}^n{U^i}f$ diverges on $ A$.


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DOI: https://doi.org/10.1090/S0002-9939-1975-0377558-X
Keywords: $ {L_p}$-space, contraction, isometry, dilation
Article copyright: © Copyright 1975 American Mathematical Society

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