A property in vector-valued function spaces

2020/07/21 by Zhao, Kexin, Tan, Dongni
#46B20 #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2007.10589

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_∞(μ,X) and L₁(μ,X).

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