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

• URL: http://arxiv.org/abs/2110.12031v2
• Date: Sun, 1 May 2022 04:24:06 GMT
• Title: Majorization and Semi-Doubly Stochastic Operators on $L^1(X)$
• Authors: Seyed Mahmoud Manjegani and Shirin Moein
• Abstract summary: This article is devoted to a study of majorization based on semi-doubly operators (denoted by $SmathcalD(L1)$) on $L1(X)$) We answer Mirsky's question and characterized the majorization by means of semi-doubly maps on $L1(X)$.
• Score: 0.0
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• 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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