On the Banach-Stone problem

Jyh-Shyang Jeang, and Ngai-Ching Wong. "On the Banach-Stone problem." Studia Mathematica 155.2 (2003): 95-105. <http://eudml.org/doc/284548>.

@article{Jyh2003,
abstract = {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 $ℓ₂^\{∞\}$ then T can be written as a weighted composition operator in the classical sense.},
author = {Jyh-Shyang Jeang, Ngai-Ching Wong},
journal = {Studia Mathematica},
keywords = {Banach–Stone theorem; strict convexity; weighted composition operator},
language = {eng},
number = {2},
pages = {95-105},
title = {On the Banach-Stone problem},
url = {http://eudml.org/doc/284548},
volume = {155},
year = {2003},
}

TY - JOUR
AU - Jyh-Shyang Jeang
AU - Ngai-Ching Wong
TI - On the Banach-Stone problem
JO - Studia Mathematica
PY - 2003
VL - 155
IS - 2
SP - 95
EP - 105
AB - 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 $ℓ₂^{∞}$ then T can be written as a weighted composition operator in the classical sense.
LA - eng
KW - Banach–Stone theorem; strict convexity; weighted composition operator
UR - http://eudml.org/doc/284548
ER -