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arXiv · 1209.0055

A Note on The Mazur-Ulam Property of Almost-CL-spaces

Dongni Tan·Rui Liu
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Abstract

We introduce the (T)-property, and prove that every Banach space with the (T)-property has the Mazur-Ulam property (briefly MUP). As its immediate applications, we obtain that almost-CL-spaces admitting a smooth point(specially, separable almost-CL-spaces) and a two-dimensional space whose unit sphere is a hexagon has the MUP. Furthermore, we discuss the stability of the spaces having the MUP by the $c_0$- and $\ell_1$-sums, and show that the space $C(K,X)$ of the vector-valued continuous functions has the the MUP, where $X$ is a separable almost-CL-space and $K$ is a compact metric space.

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Dongni Tan, Rui Liu. 2012-09-01. A Note on The Mazur-Ulam Property of Almost-CL-spaces. https://arxiv.org/abs/1209.0055

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