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)
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