Majorization and Semi-Doubly Stochastic Operators on L¹(X)

2021/10/22 by Manjegani, Seyed Mahmoud, Moein, Shirin
#FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Quantum Physics (quant-ph)

paper · doi:10.48550/arxiv.2110.12031

Abstract

This article is devoted to a study of majorization based on semi-doubly stochastic operators (denoted by SD(L¹)) on L¹(X) when X is a σ-finite measure space. We answered Mirsky's question and characterized the majorization by means of semi-doubly stochastic maps on L¹(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∈ SD(L¹)\ when f is a fixed element in L¹(X) by proving equi-integrability of S_f.

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