How far is C₀(Γ,X) with Γ discrete from C₀(K,X) spaces?

• Autorzy: Leandro Candido , Elói Medina Galego
• Języki publikacji: EN

Abstrakty

EN

For a locally compact Hausdorff space K and a Banach space X we denote by C₀(K,X) the space of X-valued continuous functions on K which vanish at infinity, provided with the supremum norm. Let n be a positive integer, Γ an infinite set with the discrete topology, and X a Banach space having non-trivial cotype. We first prove that if the nth derived set of K is not empty, then the Banach-Mazur distance between C₀(Γ,X) and C₀(K,X) is greater than or equal to 2n + 1. We also show that the Banach-Mazur distance between C₀(ℕ,X) and C([1,ωⁿk],X) is exactly 2n + 1, for any positive integers n and k. These results extend and provide a vector-valued version of some 1970 Cambern theorems, concerning the cases where n = 1 and X is the scalar field.

Kategorie tematyczne

• 46E40: Spaces of vector- and operator-valued functions
• 46B03: Isomorphic theory (including renorming) of Banach spaces
• 46E27: Spaces of measures
• 46B25: Classical Banach spaces in the general theory

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2012
• Tom: 218
• Numer: 2
• Strony: 151-163

Daty

wydano

2012

Twórcy

autor

Leandro Candido

• Department of Mathematics, IME, University of São Paulo, Rua do Matão 1010, São Paulo, Brazil

autor

Elói Medina Galego

• Department of Mathematics, University of São Paulo, IME, Rua do Matão 1010, São Paulo, Brazil

Identyfikatory

DOI

10.4064/fm218-2-3