A property in vector-valued function spaces

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 $L_{\infty }(\mu ,X)$ and $L_1(\mu ,X)$.

15 pages,0 figures

References in corpus (1)

• Extension of isometries between unit spheres of finite-dimensional polyhedral Banach spaces