Spaces of operators and c₀

• Autorzy: P. Lewis
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 46B20: Geometry and structure of normed linear spaces
• 46B25: Classical Banach spaces in the general theory
• 46B28: Spaces of operators; tensor products; approximation properties

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2001
• Tom: 145
• Numer: 3
• Strony: 213-218

Daty

wydano

2001

Twórcy

autor

P. Lewis

• Department of Mathematics, University of North Texas, Denton, TX 76203, U.S.A.

Identyfikatory

DOI

10.4064/sm145-3-3