D. Tan, X. Huang and R. Liu [Studia Math. 219 (2013)] recently introduced the notion of generalised lush (GL) spaces, which, at least for separable spaces, is a generalisation of the concept of lushness introduced by Boyko et al. [Math. Proc. Cambridge Philos. Soc. 142 (2007)]. The main result of D. Tan et al. is that every GL-space has the so called Mazur-Ulam property (MUP). In this note, we prove some further properties of GL-spaces, for example, every M-ideal in a GL-space is again a GL-space, ultraproducts of GL-spaces are again GL-spaces, and if the bidual X** of a Banach space X is GL, then X itself has the MUP.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm8192-1-2016,
author = {Jan-David Hardtke},
title = {Some remarks on generalised lush spaces},
journal = {Studia Mathematica},
volume = {231},
year = {2015},
pages = {29-44},
zbl = {06545408},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm8192-1-2016}
}
Jan-David Hardtke. Some remarks on generalised lush spaces. Studia Mathematica, Tome 231 (2015) pp. 29-44. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm8192-1-2016/