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Proceedings of the American Mathematical Society

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

 

 

Extreme invariant positive operators on $ L\sb{p}$-spaces


Author: Harald Luschgy
Journal: Proc. Amer. Math. Soc. 72 (1978), 301-304
MSC: Primary 47D20; Secondary 46E30
DOI: https://doi.org/10.1090/S0002-9939-1978-0507328-3
MathSciNet review: 507328
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Abstract: Let $ (X,\mathfrak{A},\mu )$ and $ (Y,\mathfrak{B},\nu )$ be finite positive measure spaces. In this note we present characterizations of the extreme points of the convex set of all positive linear operators $ T:{L_p}(\mu ) \to {L_q}(\nu )$ with $ T{{\mathbf{1}}_X} = {{\mathbf{1}}_Y}$ which are invariant with respect to a semigroup of positive constant preserving contractions on $ {L_p}(\mu ),1 \leqslant p < \infty ,1 \leqslant q \leqslant \infty $.


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DOI: https://doi.org/10.1090/S0002-9939-1978-0507328-3
Keywords: $ {L_p}$-spaces, extreme invariant positive linear operators, contractive semigroups, conditional expectations
Article copyright: © Copyright 1978 American Mathematical Society