Some duality results on bounded approximation properties of pairs

Eve Oja, and Silja Treialt. "Some duality results on bounded approximation properties of pairs." Studia Mathematica 217.1 (2013): 79-94. <http://eudml.org/doc/286415>.

@article{EveOja2013,
abstract = {The main result is as follows. Let X be a Banach space and let Y be a closed subspace of X. Assume that the pair $(X*,Y^\{⊥\})$ has the λ-bounded approximation property. Then there exists a net $(S_\{α\})$ of finite-rank operators on X such that $S_\{α\}(Y) ⊂ Y$ and $||S_\{α\}|| ≤ λ$ for all α, and $(S_\{α\})$ and $(S*_\{α\})$ converge pointwise to the identity operators on X and X*, respectively. This means that the pair (X,Y) has the λ-bounded duality approximation property.},
author = {Eve Oja, Silja Treialt},
journal = {Studia Mathematica},
keywords = {Banach spaces; bounded approximation property of a pair; approximation properties defined by spaces of operators; integral operators},
language = {eng},
number = {1},
pages = {79-94},
title = {Some duality results on bounded approximation properties of pairs},
url = {http://eudml.org/doc/286415},
volume = {217},
year = {2013},
}

TY - JOUR
AU - Eve Oja
AU - Silja Treialt
TI - Some duality results on bounded approximation properties of pairs
JO - Studia Mathematica
PY - 2013
VL - 217
IS - 1
SP - 79
EP - 94
AB - The main result is as follows. Let X be a Banach space and let Y be a closed subspace of X. Assume that the pair $(X*,Y^{⊥})$ has the λ-bounded approximation property. Then there exists a net $(S_{α})$ of finite-rank operators on X such that $S_{α}(Y) ⊂ Y$ and $||S_{α}|| ≤ λ$ for all α, and $(S_{α})$ and $(S*_{α})$ converge pointwise to the identity operators on X and X*, respectively. This means that the pair (X,Y) has the λ-bounded duality approximation property.
LA - eng
KW - Banach spaces; bounded approximation property of a pair; approximation properties defined by spaces of operators; integral operators
UR - http://eudml.org/doc/286415
ER -