Letand be locally compact Hausdorff spaces and let be a strictly convex Banach space of finite dimension at least 2. In this paper, we prove that if there exists an isomorphism from 0 ( , ) onto 0 ( , ) satisfyingthen and are homeomorphic. Here ( ) denotes the Schäffer constant of . Even for the classical cases = , 1 < < ∞ and ≥ 2, this result is the -valued Banach-Stone theorem via isomorphism with the largest distortion that is known so far, namely ( ) = min { 2 1∕ , 2 1−1∕ } . On the other hand, it is well known that this result is not true for = , even though and are compact Hausdorff spaces. K E Y W O R D S 0 ( , ) spaces, spaces, Schäffer constant, strictly convex spaces, vector-valued Banach-Stone theorems M S C ( 2 0 1 0 ) Primary: 46B03, 46E15; Secondary: 46B25, 46E40 996
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.