Uniform factorization for compact sets of weakly compact operators
Volume 174 / 2006
Studia Mathematica 174 (2006), 85-97
MSC: Primary 46B04, 46B20, 46B28, 46B50, 47A68, 47B07; Secondary 46B25.
DOI: 10.4064/sm174-1-7
Abstract
We prove uniform factorization results that describe the factorization of compact sets of compact and weakly compact operators via Hölder continuous homeomorphisms having Lipschitz continuous inverses. This yields, in particular, quantitative strengthenings of results of Graves and Ruess on the factorization through $\ell _p$-spaces and of Aron, Lindström, Ruess, and Ryan on the factorization through universal spaces of Figiel and Johnson. Our method is based on the isometric version of the Davis–Figiel–Johnson–Pełczyński factorization construction due to Lima, Nygaard, and Oja.
