Majorization and Semi-Doubly Stochastic Operators on $L^1(X)$

Seyed Mahmoud Manjegani; Shirin Moein

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arXiv · 2110.12031

Majorization and Semi-Doubly Stochastic Operators on $L^1(X)$

Seyed Mahmoud Manjegani·Shirin Moein

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Abstract

This article is devoted to a study of majorization based on semi-doubly stochastic operators (denoted by $S\mathcal{D}(L^1)$) on $L^1(X)$ when $X$ is a $\sigma$-finite measure space. We answered Mirsky's question and characterized the majorization by means of semi-doubly stochastic maps on $L^1(X)$. We collect some results of semi-doubly stochastic operators such as a strong relation of semi-doubly stochastic operators and integral stochastic operators, and relatively weakly compactness of $S_f=\{Sf: ~S\in S\mathcal{D}(L^1)\}$ when $f$ is a fixed element in $L^1(X)$ by proving equi-integrability of $S_f$.

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Seyed Mahmoud Manjegani, Shirin Moein. 2021-10-22. Majorization and Semi-Doubly Stochastic Operators on $L^1(X)$. https://arxiv.org/abs/2110.12031

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