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

Author(s)

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

Affiliation

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

• Document type: Journal article
• Source: Journal of Mathematical Analysis and Applications; v. 402, n. 1, p. 185-190, JUN 1 2013.
• Web of Science Citations: 1

Abstract

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)

• FAPESP's process: 12/15957-6 - On Banach spaces $C_0 (K, X)$ and the topology of $K$.
• Grantee: Leandro Candido Batista
• Support Opportunities: Scholarships in Brazil - Post-Doctoral