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 $L_1(\mu ,X)$.

arXiv comment15 pages,0 figures

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