Seminorm Related to Banach-Saks Property and Real Interpolation of Operators
Authors:
Andrzej Kryczka
Affiliation:
(1) Institute of Mathematics, M. Curie-Skłodowska University, 20-031 Lublin, Poland
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.