Generalized-lush spaces and the Mazur-Ulam property

Dongni Tan, Xujian Huang, and Rui Liu. "Generalized-lush spaces and the Mazur-Ulam property." Studia Mathematica 219.2 (2013): 139-153. <http://eudml.org/doc/285503>.

@article{DongniTan2013,
abstract = {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 $l_\{∞\}$-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.},
author = {Dongni Tan, Xujian Huang, Rui Liu},
journal = {Studia Mathematica},
keywords = {Mazur-Ulam property; isometric extension problem; lush spaces; generalized lush spaces},
language = {eng},
number = {2},
pages = {139-153},
title = {Generalized-lush spaces and the Mazur-Ulam property},
url = {http://eudml.org/doc/285503},
volume = {219},
year = {2013},
}

TY - JOUR
AU - Dongni Tan
AU - Xujian Huang
AU - Rui Liu
TI - Generalized-lush spaces and the Mazur-Ulam property
JO - Studia Mathematica
PY - 2013
VL - 219
IS - 2
SP - 139
EP - 153
AB - 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 $l_{∞}$-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.
LA - eng
KW - Mazur-Ulam property; isometric extension problem; lush spaces; generalized lush spaces
UR - http://eudml.org/doc/285503
ER -