A unified approach to the strong approximation property and the weak bounded approximation property of Banach spaces

• Autorzy: Aleksei Lissitsin
• Języki publikacji: EN

Abstrakty

EN

We consider convex versions of the strong approximation property and the weak bounded approximation property and develop a unified approach to their treatment introducing the inner and outer Λ-bounded approximation properties for a pair consisting of an operator ideal and a space ideal. We characterize this type of properties in a general setting and, using the isometric DFJP-factorization of operator ideals, provide a range of examples for this characterization, eventually answering a question due to Lima, Lima, and Oja: Are there larger Banach operator ideals than 𝒲 yielding the weak bounded approximation property?

Kategorie tematyczne

• 47L20: Operator ideals
• 46B20: Geometry and structure of normed linear spaces
• 47L07: Convex sets and cones of operators
• 47B10: Operators belonging to operator ideals (nuclear, p -summing, in the Schatten-von Neumann classes, etc.)
• 46B42: Banach lattices
• 46B28: Spaces of operators; tensor products; approximation properties

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2012
• Tom: 211
• Numer: 3
• Strony: 199-214

Daty

wydano

2012

Twórcy

autor

Aleksei Lissitsin

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

Identyfikatory

DOI

10.4064/sm211-3-2