Illinois Journal of Mathematics

On subspaces of spaces with an unconditional basis and spaces of operators

Moshe Feder

Full-text: Open access

Abstract

A reflexive Banach space $E$ has an unconditional finite dimensional expansion of the identity iff $E$ has the approximation property and $E$ is a subspace of a space with an unconditional basis. More results are given in the non-reflexive case. The results are applied to show that the non-complementation of $C(E,F)$ in $L(E,F)$ is equivalent to $C(E,F)\neq L(E,F)$ in certain cases such as: $E$ is reflexive, $E$ or $F$ has the b.a.p, and $F$ is a subspace of a space with an unconditional basis.

Article information

Source
Illinois J. Math., Volume 24, Issue 2 (1980), 196-205.

Dates
First available in Project Euclid: 20 October 2009

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1256047715

Digital Object Identifier
doi:10.1215/ijm/1256047715

Mathematical Reviews number (MathSciNet)
MR575060

Zentralblatt MATH identifier
0411.46009

Subjects
Primary: 46B15: Summability and bases [See also 46A35]
Secondary: 47D15

Citation

Feder, Moshe. On subspaces of spaces with an unconditional basis and spaces of operators. Illinois J. Math. 24 (1980), no. 2, 196--205. doi:10.1215/ijm/1256047715. https://projecteuclid.org/euclid.ijm/1256047715


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