How does the distortion of linear embedding of C-0(K) into C-0(Gamma, X) spaces depend on the height of K?

Autor(es)

Candido, Leandro ^[1] ; Galego, Eloi Medina ^[1]

Afiliação do(s) autor(es)

^[1] Univ Sao Paulo, Dept Math, IME, Sao Paulo - Brazil

• Tipo de documento: Artigo Científico
• Fonte: Journal of Mathematical Analysis and Applications; v. 402, n. 1, p. 185-190, JUN 1 2013.
• Citações Web of Science: 1

Resumo

Let C-0(K) denote the space of all continuous scalar-valued functions defined on the locally compact Hausdorff space K which vanish at infinity, provided with the supremum norm. Let Gamma be an infinite set endowed with discrete topology and X a Banach space. We denote by C-0(Gamma, X) the Banach space of X-valued functions defined on Gamma which vanish at infinity, provided with the supremum norm. In this paper, we prove that, if X has non-trivial cotype and there exists a linear isomorphism T from C-0(K) into C-0(Gamma, X), then K has finite height ht(K), and the distortion parallel to T parallel to parallel to T-1 parallel to is greater than or equal to 2 ht(K) - 1. The statement of this theorem is optimal and improves a 1970 result of Gordon. (C) 2013 Elsevier Inc. All rights reserved. (AU)

• Processo FAPESP: 12/15957-6 - Sobre os espaços de Banach $C_0(K,X)$ e a topologia de $K$.
• Beneficiário: Leandro Candido Batista
• Modalidade de apoio: Bolsas no Brasil - Pós-Doutorado