Abstract
We introduce the arithmetic separation of a sequence—a geometric characteristic for bounded sequences in a Banach space which describes the Banach-Saks property. We define an operator seminorm vanishing for operators with the Banach-Saks property. We prove quantitative stability of the seminorm for a class of operators acting between lp-sums of Banach spaces. We show logarithmically convex-type estimates of the seminorm for operators interpolated by the real method of Lions and Peetre.
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