Randomized operators on \({n\times n}\) matrices and applications
type: Item
instance of: scholarly article
title: Randomized operators on \({n\times n}\) matrices and applications
zbMATH Open document ID: 1397.46023
published in: Integral Equations and Operator Theory
publication date: 2017-04-27T00:00:00Z
review text: Combinatorial and probabilistic inequalities have turned out to be useful in the local theory of Banach spaces, especially when studying the local structure of \(L_p\) spaces. Key results in this direction go back to the works of \textit{S. Kwapién} and \textit{C. Schütt} [Stud. Math. 82, 81--106 (1985; Zbl 0579.46013)] and have later been generalized and successfully applied by \textit{S. Montgomery-Smith} [Isr. J. Math. 131, 51--60 (2002; Zbl 1010.60041)], \textit{J. Prochno} and \textit{C. Schütt} [Stud. Math. 211, No. 1, 21--39 (2012; Zbl 1278.46018)], \textit{J. Prochno} [Banach J. Math. Anal. 7, No. 1, 132--141 (2013; Zbl 1272.46008)], and \textit{R. Lechner} et al. [J. Theor. Probab. 30, No. 4, 1445--1470 (2017; Zbl 1382.62023)]. Here, the authors study these estimates in the general setting of rearrangement invariant function and sequence spaces and identify the class of function spaces in which such estimates hold. In particular, they prove that their results are sharp, and, as an application, provide an alternative proof for a result of \textit{Y. Raynaud} and \textit{C. Schütt} [Stud. Math. 89, No.~1, 27--35 (1988; Zbl 0659.46022)] on symmetric subspaces of \(L_1\).
reviewed by: Joscha Prochno
Mathematics Subject Classification ID: 46E30
Mathematics Subject Classification ID: 46B42
Mathematics Subject Classification ID: 46B09
Mathematics Subject Classification ID: 46B45
zbMATH DE Number: 6708451
zbMATH Keywords: rearrangement invariant space
zbMATH Keywords: symmetric sequence space
zbMATH Keywords: independent random variables
zbMATH Keywords: doubly stochastic matrix
zbMATH Keywords: Orlicz space
author: Sergey Astashkin
author: Fedor Sukochev
MaRDI profile type: Publication
full work available at URL: s00020-016-2322-1
OpenAlex ID: W2528821631
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DOI: 10.1007/S00020-016-2322-1
description: scientific article; zbMATH DE number 6708451