Ideals of finite rank operators, intersection properties of balls, and the approximation property

Åsvald Lima; Eve Oja

Studia Mathematica (1999)

  • Volume: 133, Issue: 2, page 175-186
  • ISSN: 0039-3223

Abstract

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We characterize the approximation property of Banach spaces and their dual spaces by the position of finite rank operators in the space of compact operators. In particular, we show that a Banach space E has the approximation property if and only if for all closed subspaces F of c 0 , the space ℱ(F,E) of finite rank operators from F to E has the n-intersection property in the corresponding space K(F,E) of compact operators for all n, or equivalently, ℱ(F,E) is an ideal in K(F,E).

How to cite

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Lima, Åsvald, and Oja, Eve. "Ideals of finite rank operators, intersection properties of balls, and the approximation property." Studia Mathematica 133.2 (1999): 175-186. <http://eudml.org/doc/216612>.

@article{Lima1999,
abstract = {We characterize the approximation property of Banach spaces and their dual spaces by the position of finite rank operators in the space of compact operators. In particular, we show that a Banach space E has the approximation property if and only if for all closed subspaces F of $c_0$, the space ℱ(F,E) of finite rank operators from F to E has the n-intersection property in the corresponding space K(F,E) of compact operators for all n, or equivalently, ℱ(F,E) is an ideal in K(F,E).},
author = {Lima, Åsvald, Oja, Eve},
journal = {Studia Mathematica},
keywords = {approximation property; finite rank operators; -intersection property; compact operators},
language = {eng},
number = {2},
pages = {175-186},
title = {Ideals of finite rank operators, intersection properties of balls, and the approximation property},
url = {http://eudml.org/doc/216612},
volume = {133},
year = {1999},
}

TY - JOUR
AU - Lima, Åsvald
AU - Oja, Eve
TI - Ideals of finite rank operators, intersection properties of balls, and the approximation property
JO - Studia Mathematica
PY - 1999
VL - 133
IS - 2
SP - 175
EP - 186
AB - We characterize the approximation property of Banach spaces and their dual spaces by the position of finite rank operators in the space of compact operators. In particular, we show that a Banach space E has the approximation property if and only if for all closed subspaces F of $c_0$, the space ℱ(F,E) of finite rank operators from F to E has the n-intersection property in the corresponding space K(F,E) of compact operators for all n, or equivalently, ℱ(F,E) is an ideal in K(F,E).
LA - eng
KW - approximation property; finite rank operators; -intersection property; compact operators
UR - http://eudml.org/doc/216612
ER -

References

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