Asymptotic domination of operators on Köthe function spaces and convergence of sequences | Zendy

Sánchez Pérez E. A. | Zendy

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Asymptotic domination of operators on Köthe function spaces and convergence of sequences

Author(s) -

Sánchez Pérez E. A.

Publication year - 2006

Publication title -

mathematische nachrichten

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.913

H-Index - 50

eISSN - 1522-2616

pISSN - 0025-584X

DOI - 10.1002/mana.200410448

Subject(s) - mathematics , spectral theorem , pure mathematics , operator norm , function (biology) , norm (philosophy) , operator theory , function space , convergence (economics) , interpolation (computer graphics) , discrete mathematics , animation , computer graphics (images) , evolutionary biology , economic growth , political science , computer science , law , economics , biology

We study the asymptotic behavior of Maurey–Rosenthal type dominations for operators on Köthe function spaces which satisfy norm inequalities that define weak q ‐concavity properties. In particular, we define and study two new classes of operators that we call α ‐almost q ‐concave and q α ‐concave operators (1 ≤ q < ∞, 0 ≤ α < 1). We also provide a factorization theorem through real interpolation spaces for q α ‐concave operators. We also discuss some direct consequences of these results regarding the strong convergence of sequences on Köthe function spaces. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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