Spaces of operators and c₀

P. Lewis. "Spaces of operators and c₀." Studia Mathematica 145.3 (2001): 213-218. <http://eudml.org/doc/284631>.

@article{P2001,
abstract = {Bessaga and Pełczyński showed that if c₀ embeds in the dual X* of a Banach space X, then ℓ¹ embeds complementably in X, and $ℓ^\{∞\}$ 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 $ℓ^\{∞\}$ embeds in L(X,Y), and ℓ¹ embeds complementably in $X ⊗_\{γ \} Y*$. Applications to embeddings of c₀ in various spaces of operators are given.},
author = {P. Lewis},
journal = {Studia Mathematica},
keywords = {imbedding of Banach spaces; complementation; spaces of operators},
language = {eng},
number = {3},
pages = {213-218},
title = {Spaces of operators and c₀},
url = {http://eudml.org/doc/284631},
volume = {145},
year = {2001},
}

TY - JOUR
AU - P. Lewis
TI - Spaces of operators and c₀
JO - Studia Mathematica
PY - 2001
VL - 145
IS - 3
SP - 213
EP - 218
AB - Bessaga and Pełczyński showed that if c₀ embeds in the dual X* of a Banach space X, then ℓ¹ embeds complementably in X, and $ℓ^{∞}$ 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 $ℓ^{∞}$ embeds in L(X,Y), and ℓ¹ embeds complementably in $X ⊗_{γ } Y*$. Applications to embeddings of c₀ in various spaces of operators are given.
LA - eng
KW - imbedding of Banach spaces; complementation; spaces of operators
UR - http://eudml.org/doc/284631
ER -