An ideal characterization of when a subspace of certain Banach spaces has the metric compact approximation property

J. Cabello; E. Nieto

Studia Mathematica (1998)

  • Volume: 129, Issue: 2, page 185-196
  • ISSN: 0039-3223

Abstract

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C.-M. Cho and W. B. Johnson showed that if a subspace E of ℓ p , 1 < p < ∞, has the compact approximation property, then K(E) is an M-ideal in ℒ(E). We prove that for every r,s ∈ ]0,1] with r 2 + s 2 < 1 , the James space can be provided with an equivalent norm such that an arbitrary subspace E has the metric compact approximation property iff there is a norm one projection P on ℒ(E)* with Ker P = K(E)⊥ satisfying ∥⨍∥ ≥ r∥Pf∥ + s∥φ - Pf∥ ∀⨍ ∈ ℒ(E)*. A similar result is proved for subspaces of upper p-spaces (e.g. Lorentz sequence spaces d(w, p) and certain renormings of L p ).

How to cite

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Cabello, J., and Nieto, E.. "An ideal characterization of when a subspace of certain Banach spaces has the metric compact approximation property." Studia Mathematica 129.2 (1998): 185-196. <http://eudml.org/doc/216498>.

@article{Cabello1998,
author = {Cabello, J., Nieto, E.},
journal = {Studia Mathematica},
keywords = {ideal characterization; -ideal; metric compact approximation property; upper -spaces; Lorentz sequence spaces; renormings of },
language = {eng},
number = {2},
pages = {185-196},
title = {An ideal characterization of when a subspace of certain Banach spaces has the metric compact approximation property},
url = {http://eudml.org/doc/216498},
volume = {129},
year = {1998},
}

TY - JOUR
AU - Cabello, J.
AU - Nieto, E.
TI - An ideal characterization of when a subspace of certain Banach spaces has the metric compact approximation property
JO - Studia Mathematica
PY - 1998
VL - 129
IS - 2
SP - 185
EP - 196
LA - eng
KW - ideal characterization; -ideal; metric compact approximation property; upper -spaces; Lorentz sequence spaces; renormings of
UR - http://eudml.org/doc/216498
ER -

References

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