Uniform factorization for compact sets of weakly compact operators

• Autorzy: Kristel Mikkor , Eve Oja
• Języki publikacji: EN

Abstrakty

EN

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 $ℓ_{p}$-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.

Kategorie tematyczne

• 47A68: Factorization theory (including Wiener-Hopf and spectral factorizations)
• 46B20: Geometry and structure of normed linear spaces
• 46B04: Isometric theory of Banach spaces
• 47B07: Operators defined by compactness properties
• 46B50: Compactness in Banach (or normed) spaces
• 46B25: Classical Banach spaces in the general theory
• 46B28: Spaces of operators; tensor products; approximation properties

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2006
• Tom: 174
• Numer: 1
• Strony: 85-97

Daty

wydano

2006

Twórcy

autor

Kristel Mikkor

• Faculty of Mathematics and Computer Science, Tartu University, J. Liivi 2, EE-50409 Tartu, Estonia

autor

Eve Oja

• Faculty of Mathematics and Computer Science, Tartu University, J. Liivi 2, EE-50409 Tartu, Estonia

Identyfikatory

DOI

10.4064/sm174-1-7