Some remarks on generalised lush spaces

Jan-David Hardtke

Studia Mathematica (2015)

  • Volume: 231, Issue: 1, page 29-44
  • ISSN: 0039-3223

Abstract

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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.

How to cite

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Jan-David Hardtke. "Some remarks on generalised lush spaces." Studia Mathematica 231.1 (2015): 29-44. <http://eudml.org/doc/285617>.

@article{Jan2015,
abstract = { 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. },
author = {Jan-David Hardtke},
journal = {Studia Mathematica},
keywords = {generalised lush spaces; lush spaces; -ideals; absolute norms; -ideals; Mazur-Ulam property; ultraproducts},
language = {eng},
number = {1},
pages = {29-44},
title = {Some remarks on generalised lush spaces},
url = {http://eudml.org/doc/285617},
volume = {231},
year = {2015},
}

TY - JOUR
AU - Jan-David Hardtke
TI - Some remarks on generalised lush spaces
JO - Studia Mathematica
PY - 2015
VL - 231
IS - 1
SP - 29
EP - 44
AB - 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.
LA - eng
KW - generalised lush spaces; lush spaces; -ideals; absolute norms; -ideals; Mazur-Ulam property; ultraproducts
UR - http://eudml.org/doc/285617
ER -

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