We introduce a new class of Banach spaces, called generalized-lush spaces (GL-spaces for short), which contains almost-CL-spaces, separable lush spaces (in particular, separable C-rich subspaces of C(K)), and even the two-dimensional space with hexagonal norm. We find that the space C(K,E) of vector-valued continuous functions is a GL-space whenever E is, and show that the set of GL-spaces is stable under c₀-, l₁- and -sums. As an application, we prove that the Mazur-Ulam property holds for a larger class of Banach spaces, called local-GL-spaces, including all lush spaces and GL-spaces. Furthermore, we generalize the stability properties of GL-spaces to local-GL-spaces. From this, we can obtain many examples of Banach spaces having the Mazur-Ulam property.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm219-2-4,
author = {Dongni Tan and Xujian Huang and Rui Liu},
title = {Generalized-lush spaces and the Mazur-Ulam property},
journal = {Studia Mathematica},
volume = {215},
year = {2013},
pages = {139-153},
zbl = {1296.46009},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm219-2-4}
}
Dongni Tan; Xujian Huang; Rui Liu. Generalized-lush spaces and the Mazur-Ulam property. Studia Mathematica, Tome 215 (2013) pp. 139-153. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm219-2-4/