Sobczyk's theorem and the Bounded Approximation Property

• Autorzy: Jesús M. F. Castillo , Yolanda Moreno
• Języki publikacji: EN

Abstrakty

EN

Sobczyk's theorem asserts that every c₀-valued operator defined on a separable Banach space can be extended to every separable superspace. This paper is devoted to obtaining the most general vector valued version of the theorem, extending and completing previous results of Rosenthal, Johnson-Oikhberg and Cabello. Our approach is homological and nonlinear, transforming the problem of extension of operators into the problem of approximating z-linear maps by linear maps.

Kategorie tematyczne

• 46T99: None of the above, but in this section
• 46M18: Homological methods (exact sequences, right inverses, lifting, etc.)
• 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: 2010
• Tom: 201
• Numer: 1
• Strony: 1-19

Daty

wydano

2010

Twórcy

autor

Jesús M. F. Castillo

• Departamento de Matemáticas, Universidad de Extremadura, Avenida de Elvas, 06071 Badajoz, Spain

autor

Yolanda Moreno

• Departamento de Mateméticas, Universidad de Extremadura, Avenida de Elvas, 06071-Badajoz, Spain

Identyfikatory

DOI

10.4064/sm201-1-1