Media type: E-Article Title: Asymptotic domination of operators on Köthe function spaces and convergence of sequences Contributor: Sánchez Pérez, E. A. imprint: Wiley, 2006 Published in: Mathematische Nachrichten Language: English DOI: 10.1002/mana.200410448 ISSN: 0025-584X; 1522-2616 Keywords: General Mathematics Origination: Footnote: Description: <jats:title>Abstract</jats:title><jats:p>We study the asymptotic behavior of Maurey–Rosenthal type dominations for operators on Köthe function spaces which satisfy norm inequalities that define weak <jats:italic>q</jats:italic> ‐concavity properties. In particular, we define and study two new classes of operators that we call <jats:italic>α</jats:italic> ‐almost <jats:italic>q</jats:italic> ‐concave and <jats:italic>q<jats:sub>α</jats:sub></jats:italic> ‐concave operators (1 ≤ <jats:italic>q</jats:italic> < ∞, 0 ≤ <jats:italic>α</jats:italic> < 1). We also provide a factorization theorem through real interpolation spaces for <jats:italic>q<jats:sub>α</jats:sub></jats:italic> ‐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)</jats:p>