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

Abstract

AbstractWe 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 qα ‐concave operators (1 ≤ q < ∞, 0 ≤ α < 1). We also provide a factorization theorem through real interpolation spaces for qα ‐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)