On extensions of c(0)-valued operators

Author(s)

Correa, Claudia ^[1] ; Tausk, Daniel V. ^[1]

Affiliation

^[1] Univ Sao Paulo, Dept Matemat, BR-05508 Sao Paulo - Brazil

• Document type: Journal article
• Source: Journal of Mathematical Analysis and Applications; v. 405, n. 2, p. 400-408, SEP 15 2013.
• Web of Science Citations: 2

Abstract

We study pairs of Banach spaces (X, Y), with Y subset of X, for which the thesis of Sobczyk's theorem holds, namely, such that every bounded c(0)-valued operator defined in Y extends to X. We are mainly concerned with the case when X is a C(K) space and Y C(L) is a Banach subalgebra of C(K). The main result of the article states that, if K is a compact line and L is countable, then every bounded c(0)-valued operator defined in C(L) extends to C(K). (c) 2013 Elsevier Inc. All rights reserved. (AU)

• FAPESP's process: 10/17853-8 - Set-theoretic topological methods on operators on Banach spaces of the form C(K)
• Grantee: Claudia Correa de Andrade Oliveira
• Support Opportunities: Scholarships in Brazil - Doctorate