Geodesic
Sobczyk's theorem and the Bounded Approximation Property
Jesús M. F. Castillo1 ; Yolanda Moreno2
1 Departamento de Matemáticas Universidad de Extremadura Avenida de Elvas 06071 Badajoz, Spain
2 Departamento de Mateméticas Universidad de Extremadura Avenida de Elvas 06071-Badajoz, Spain
Studia Mathematica, Tome 201 (2010) no. 1, pp. 1-19

Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences

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.
DOI : 10.4064/sm201-1-1
Keywords: sobczyks theorem asserts every valued operator defined separable banach space extended every separable superspace paper devoted obtaining general vector valued version theorem extending completing previous results rosenthal johnson oikhberg cabello approach homological nonlinear transforming problem extension operators problem approximating z linear maps linear maps

Jesús M. F. Castillo 1 ; Yolanda Moreno 2

1 Departamento de Matemáticas Universidad de Extremadura Avenida de Elvas 06071 Badajoz, Spain
2 Departamento de Mateméticas Universidad de Extremadura Avenida de Elvas 06071-Badajoz, Spain 
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Jesús M. F. Castillo; Yolanda Moreno. Sobczyk's theorem and
 the Bounded Approximation Property. Studia Mathematica, Tome 201 (2010) no. 1, pp. 1-19. doi: 10.4064/sm201-1-1

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