Alternating sequences with nonpositive operators

Akcoglu, M. A.

doi:10.1090/S0002-9939-1988-0943791-8

Alternating sequences with nonpositive operators
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by M. A. Akcoglu

Proc. Amer. Math. Soc. 104 (1988), 1124-1130

DOI: https://doi.org/10.1090/S0002-9939-1988-0943791-8

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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, $1 \leq p \leq \infty ({\text {i}}{\text {.e}}{\text {.}}{\left \| {{T_n}} \right \|_p} \leq 1)$. 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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Topics in harmonic analysis