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Proceedings of the American Mathematical Society

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

 
 

 

Extreme invariant positive operators on $L_{p}$-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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Keywords: <IMG WIDTH="29" HEIGHT="38" ALIGN="MIDDLE" BORDER="0" SRC="images/img1.gif" ALT="${L_p}$">-spaces, extreme invariant positive linear operators, contractive semigroups, conditional expectations
Article copyright: © Copyright 1978 American Mathematical Society