Some remarks on generalised lush spaces

• Autorzy: Jan-David Hardtke
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 46B20: Geometry and structure of normed linear spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2015
• Tom: 231
• Numer: 1
• Strony: 29-44

Daty

wydano

2015

Twórcy

autor

Jan-David Hardtke

• Department of Mathematics, Freie Universität Berlin, Arnimallee 6, 14195 Berlin, Germany

Identyfikatory

DOI

10.4064/sm8192-1-2016