Year: 2020
Type: preprint
Abstract: This paper deals with a property which is equivalent to generalised-lushness for separable spaces. It thus may be seemed as a geometrical property of a Banach space which ensures the space to have the Mazur-Ulam property. We prove that if a Banach space $X$ enjoys this property if and only if $C(K,X)$ enjoys this property. We also show the same result holds for $L_\infty(μ,X)$ and $L_1(μ,X)$.
Source: arXiv (Cornell University)
Authors: Zhao, Kexin, Tan, Dongni
Institution: Tianjin University of Technology
Language: English
Topic: Advanced Banach Space Theory
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W3044545613