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Proceedings of the American Mathematical Society

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

 

 

Pointwise induced operators on $ L\sb{p}$-spaces


Author: Anzelm Iwanik
Journal: Proc. Amer. Math. Soc. 58 (1976), 173-178
MSC: Primary 47B37; Secondary 46E30
DOI: https://doi.org/10.1090/S0002-9939-1976-0412883-6
MathSciNet review: 0412883
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Abstract: In this note we present a characterization of pointwise induced operators on $ {L_p}$-spaces with finite measures, $ 1 \leq p < \infty $. An operator $ P$ is pointwise induced if and only if $ \vert Pu\vert = P\vert u\vert$ and $ P1 = 1$. As an application we obtain a characterization of the linear positive isometries mapping 1 into 1.


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DOI: https://doi.org/10.1090/S0002-9939-1976-0412883-6
Keywords: $ {L_p}$-space, nonsingular transformation, nonnegative operator, Borel space, quotient Boolean $ \sigma $-algebra
Article copyright: © Copyright 1976 American Mathematical Society