Sobczyk's theorem and the Bounded Approximation Property

Tom 201 / 2010

Jesús M. F. Castillo, Yolanda Moreno Studia Mathematica 201 (2010), 1-19 MSC: Primary 46M18, 46B25, 46T99; Secondary 46B28. DOI: 10.4064/sm201-1-1

Streszczenie

Sobczyk's theorem asserts that every $c_0$-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.

Autorzy

  • Jesús M. F. CastilloDepartamento de Matemáticas
    Universidad de Extremadura
    Avenida de Elvas
    06071 Badajoz, Spain
    e-mail
  • Yolanda MorenoDepartamento de Mateméticas
    Universidad de Extremadura
    Avenida de Elvas
    06071-Badajoz, Spain
    e-mail

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