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Seminorm Related to Banach-Saks Property and Real Interpolation of Operators

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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 l p -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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  1. Institute of Mathematics, M. Curie-Skłodowska University, 20-031, Lublin, Poland

    Andrzej Kryczka

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  1. Andrzej Kryczka
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Correspondence to Andrzej Kryczka.

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Kryczka, A. Seminorm Related to Banach-Saks Property and Real Interpolation of Operators. Integr. equ. oper. theory 61, 559–572 (2008). https://doi.org/10.1007/s00020-008-1603-8

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  • DOI: https://doi.org/10.1007/s00020-008-1603-8

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