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arXiv · 2406.08095

Substochastic operators in symmetric spaces

Maciej Ciesielski·Grzegorz Lewicki
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Abstract

First, we solve a crucial problem under which conditions increasing uniform K-monotonicity is equivalent to lower locally uniform K-monotonicity. Next, we investigate properties of substochastic operators on $L^1+L^\infty$ with applications. Namely, we show that a countable infinite combination of substochastic operators is also substochastic. Using K-monotonicity properties, we prove several theorems devoted to the convergence of the sequence of substochastic operators in the norm of a symmetric space E under addition assumption on E. In our final discussion we focus on compactness of admissible operators for arbitrary Banach couples.

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Maciej Ciesielski, Grzegorz Lewicki. 2024-06-12. Substochastic operators in symmetric spaces. https://arxiv.org/abs/2406.08095

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