Generalized-lush spaces and the Mazur-Ulam property

• Autorzy: Dongni Tan , Xujian Huang , Rui Liu
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 46A22: Theorems of Hahn-Banach type; extension and lifting of functionals and operators
• 46B20: Geometry and structure of normed linear spaces
• 46B04: Isometric theory of Banach spaces

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2013
• Tom: 219
• Numer: 2
• Strony: 139-153

Daty

wydano

2013

Twórcy

autor

Dongni Tan

• Department of Mathematics, Tianjin University of Technology, 300384 Tianjin, China

autor

Xujian Huang

• Department of Mathematics, Tianjin University of Technology, 300384 Tianjin, China

autor

Rui Liu

• Department of Mathematics and LPMC, Nankai University, 300071 Tianjin, China

Identyfikatory

DOI

10.4064/sm219-2-4