Sobczyk's theorem and the Bounded Approximation Property
Volume 201 / 2010
Studia Mathematica 201 (2010), 1-19
MSC: Primary 46M18, 46B25, 46T99; Secondary 46B28.
DOI: 10.4064/sm201-1-1
Abstract
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.
