On the compact approximation property

Vegard Lima, Åsvald Lima, and Olav Nygaard. "On the compact approximation property." Studia Mathematica 160.2 (2004): 185-200. <http://eudml.org/doc/284625>.

@article{VegardLima2004,
abstract = {We show that a Banach space X has the compact approximation property if and only if for every Banach space Y and every weakly compact operator T: Y → X, the space = S ∘ T: S compact operator on X is an ideal in = span(,T) if and only if for every Banach space Y and every weakly compact operator T: Y → X, there is a net $(S_γ)$ of compact operators on X such that $sup_\{γ\}||S_\{γ\}T|| ≤ ||T||$ and $S_\{γ\} → I_\{X\}$ in the strong operator topology. Similar results for dual spaces are also proved.},
author = {Vegard Lima, Åsvald Lima, Olav Nygaard},
journal = {Studia Mathematica},
keywords = {compact approximation property; spaces of operators; ideals in Banach spaces},
language = {eng},
number = {2},
pages = {185-200},
title = {On the compact approximation property},
url = {http://eudml.org/doc/284625},
volume = {160},
year = {2004},
}

TY - JOUR
AU - Vegard Lima
AU - Åsvald Lima
AU - Olav Nygaard
TI - On the compact approximation property
JO - Studia Mathematica
PY - 2004
VL - 160
IS - 2
SP - 185
EP - 200
AB - We show that a Banach space X has the compact approximation property if and only if for every Banach space Y and every weakly compact operator T: Y → X, the space = S ∘ T: S compact operator on X is an ideal in = span(,T) if and only if for every Banach space Y and every weakly compact operator T: Y → X, there is a net $(S_γ)$ of compact operators on X such that $sup_{γ}||S_{γ}T|| ≤ ||T||$ and $S_{γ} → I_{X}$ in the strong operator topology. Similar results for dual spaces are also proved.
LA - eng
KW - compact approximation property; spaces of operators; ideals in Banach spaces
UR - http://eudml.org/doc/284625
ER -