Schauder bases and the bounded approximation property in separable Banach spaces

Jorge Mujica, and Daniela M. Vieira. "Schauder bases and the bounded approximation property in separable Banach spaces." Studia Mathematica 196.1 (2010): 1-12. <http://eudml.org/doc/284847>.

@article{JorgeMujica2010,
abstract = {Let E be a separable Banach space with the λ-bounded approximation property. We show that for each ϵ > 0 there is a Banach space F with a Schauder basis such that E is isometrically isomorphic to a 1-complemented subspace of F and, moreover, the sequence (Tₙ) of canonical projections in F has the properties $sup_\{n∈ ℕ \} ||Tₙ|| ≤ λ + ϵ$ and $limsup_\{n→ ∞\} ||Tₙ|| ≤ λ$. This is a sharp quantitative version of a classical result obtained independently by Pełczyński and by Johnson, Rosenthal and Zippin.},
author = {Jorge Mujica, Daniela M. Vieira},
journal = {Studia Mathematica},
keywords = {separable Banach spaces; bounded approximation property; Schauder basis; weakly continuous holomorphic functions},
language = {eng},
number = {1},
pages = {1-12},
title = {Schauder bases and the bounded approximation property in separable Banach spaces},
url = {http://eudml.org/doc/284847},
volume = {196},
year = {2010},
}

TY - JOUR
AU - Jorge Mujica
AU - Daniela M. Vieira
TI - Schauder bases and the bounded approximation property in separable Banach spaces
JO - Studia Mathematica
PY - 2010
VL - 196
IS - 1
SP - 1
EP - 12
AB - Let E be a separable Banach space with the λ-bounded approximation property. We show that for each ϵ > 0 there is a Banach space F with a Schauder basis such that E is isometrically isomorphic to a 1-complemented subspace of F and, moreover, the sequence (Tₙ) of canonical projections in F has the properties $sup_{n∈ ℕ } ||Tₙ|| ≤ λ + ϵ$ and $limsup_{n→ ∞} ||Tₙ|| ≤ λ$. This is a sharp quantitative version of a classical result obtained independently by Pełczyński and by Johnson, Rosenthal and Zippin.
LA - eng
KW - separable Banach spaces; bounded approximation property; Schauder basis; weakly continuous holomorphic functions
UR - http://eudml.org/doc/284847
ER -