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Spaces of operators and c₀

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Lewis P.

Studia Mathematica

2001

tom 145

nr 3

213-218

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.

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1 Studia Mathematica

1 Lewis P.

1 2001

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Spaces of operators and c₀