Randomized operators on \({n\times n}\) matrices and applications
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 \(L_1\).
scientific article; zbMATH DE number 6708451
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