A simplified and unified generalization of some majorization results

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:478

Article

Moein, Shirin^1,2  Pereira, Rajesh²  Plosker, Sarah^2,3 

[1] Isfahan Univ Technol, Dept Math Sci, Esfahan 8415683111, Iran

[2] Univ Guelph, Dept Math & Stat, Guelph, ON N1G 2W1, Canada

[3] Brandon Univ, Dept Math & Comp Sci, Brandon, MB R7A 6A9, Canada

关键词: Matrix majorization;    Multivariate majorization;    Sublinear functionals;    Convex functionals;    Stochastic operators;    Markov operators;   

DOI  :  10.1016/j.jmaa.2019.05.065

来源: Elsevier

【 摘 要 】

We consider positive, integral-preserving linear operators acting on L-1 space, known as stochastic operators or Markov operators. We show that, on finite-dimensional spaces, any stochastic operator can be approximated by a sequence of stochastic integral operators (such operators arise naturally when considering matrix majorization in L-1). We collect a number of results for vector-valued functions on L-1, simplifying some proofs found in the literature. In particular, matrix majorization and multivariate majorization are related in R-n. In R, these are also equivalent to convex function inequalities. (C) 2019 Elsevier Inc. All rights reserved.

【 授权许可】

Free