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Proceedings of the American Mathematical Society

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

 

 

Alternating sequences with nonpositive operators


Author: M. A. Akcoglu
Journal: Proc. Amer. Math. Soc. 104 (1988), 1124-1130
MSC: Primary 47A35; Secondary 28D05, 47B38
DOI: https://doi.org/10.1090/S0002-9939-1988-0943791-8
MathSciNet review: 943791
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Abstract: Let $ ({T_n})$ be a sequence of linear operators acting on complex valued functions on a $ \sigma $-finite measure space. Assume that each $ {T_n}$ contracts all the $ p$-norms, $ 1 \leq p \leq \infty ({\text{i}}{\text{.e}}{\text{.}}{\left\Vert {{T_n}} \right\Vert _p} \leq 1)$. It is shown that a.e. $ {\lim _n}T_1^ * \cdots T_n^ * {T_n} \cdots {T_1}f$ exists for each $ {L_p}$ function $ f,1 < p < \infty $.


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DOI: https://doi.org/10.1090/S0002-9939-1988-0943791-8
Keywords: Contractions of $ {L_p}$ spaces, maximal inequalities
Article copyright: © Copyright 1988 American Mathematical Society