Bessaga and Pełczyński showed that if c₀ embeds in the dual X* of a Banach space X, then ℓ¹ embeds complementably in X, and embeds as a subspace of X*. In this note the Diestel-Faires theorem and techniques of Kalton are used to show that if X is an infinite-dimensional Banach space, Y is an arbitrary Banach space, and c₀ embeds in L(X,Y), then embeds in L(X,Y), and ℓ¹ embeds complementably in . Applications to embeddings of c₀ in various spaces of operators are given.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm145-3-3,
author = {P. Lewis},
title = {Spaces of operators and c0},
journal = {Studia Mathematica},
volume = {147},
year = {2001},
pages = {213-218},
zbl = {0986.46011},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm145-3-3}
}
P. Lewis. Spaces of operators and c₀. Studia Mathematica, Tome 147 (2001) pp. 213-218. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm145-3-3/