Let X and Y be locally compact Hausdorff spaces, let E and F be Banach spaces, and let T be a linear isometry from C₀(X,E) into C₀(Y,F). We provide three new answers to the Banach-Stone problem: (1) T can always be written as a generalized weighted composition operator if and only if F is strictly convex; (2) if T is onto then T can be written as a weighted composition operator in a weak sense; and (3) if T is onto and F does not contain a copy of then T can be written as a weighted composition operator in the classical sense.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm155-2-1,
author = {Jyh-Shyang Jeang and Ngai-Ching Wong},
title = {On the Banach-Stone problem},
journal = {Studia Mathematica},
volume = {157},
year = {2003},
pages = {95-105},
zbl = {1056.46011},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm155-2-1}
}
Jyh-Shyang Jeang; Ngai-Ching Wong. On the Banach-Stone problem. Studia Mathematica, Tome 157 (2003) pp. 95-105. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm155-2-1/