An ideal characterization of when a subspace of certain Banach spaces has the metric compact approximation property
Studia Mathematica, Tome 129 (1998) no. 2, pp. 185-196
Voir la notice de l'article provenant de la source Institute of Mathematics Polish Academy of Sciences
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 $L^p$).
@article{10_4064_sm_129_2_185_196,
author = {J. C. Cabello},
title = {An ideal characterization of when a subspace of certain {Banach} spaces has the metric compact approximation property},
journal = {Studia Mathematica},
pages = {185--196},
publisher = {mathdoc},
volume = {129},
number = {2},
year = {1998},
doi = {10.4064/sm-129-2-185-196},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/sm-129-2-185-196/}
}
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J. C. Cabello. An ideal characterization of when a subspace of certain Banach spaces has the metric compact approximation property. Studia Mathematica, Tome 129 (1998) no. 2, pp. 185-196. doi: 10.4064/sm-129-2-185-196
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