naa a22 4500 510782272 CHVBK 20180411083251.0 cr unu---uuuuu 180411e20131101xx s 000 0 eng 10.1007/s11856-013-0019-6 doi (NATIONALLICENCE)springer-10.1007/s11856-013-0019-6 On the bounded approximation property in Banach spaces [Elektronische Daten] [Jesús Castillo, Yolanda Moreno] We prove that the kernel of a quotient operator from an L 1-space onto a Banach space X with the Bounded Approximation Property (BAP) has the BAP. This completes earlier results of Lusky-case ℓ 1-and Figiel, Johnson and Pełczyński-case X* separable. Given a Banach space X, we show that if the kernel of a quotient map from some L 1-space onto X has the BAP, then every kernel of every quotient map from any L 1-space onto X has the BAP. The dual result for L ∞-spaces also holds: if for some L ∞-space E some quotient E/X has the BAP, then for every L ∞-space E every quotient E/X has the BAP. Hebrew University Magnes Press, 2013 Castillo Jesús Departamento de Matemáticas, Universidad de Extremadura, Avenida de Elvas s/n, 06011, Badajoz, Spain aut Moreno Yolanda Escuela Politécnica, Universidad de Extremadura, Avenida de la Universidad s/n, 10071, Cáceres, Spain aut Israel Journal of Mathematics Springer US; http://www.springer-ny.com 198/1(2013-11-01), 243-259 0021-2172 198:1<243 2013 198 11856 https://doi.org/10.1007/s11856-013-0019-6 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s11856-013-0019-6 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Castillo Jesús Departamento de Matemáticas, Universidad de Extremadura, Avenida de Elvas s/n, 06011, Badajoz, Spain aut NATIONALLICENCE 700 1- Moreno Yolanda Escuela Politécnica, Universidad de Extremadura, Avenida de la Universidad s/n, 10071, Cáceres, Spain aut NATIONALLICENCE 773 0- Israel Journal of Mathematics Springer US; http://www.springer-ny.com 198/1(2013-11-01), 243-259 0021-2172 198:1<243 2013 198 11856 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer