We introduce the (T)-property, and prove that every Banach space with the(T)-property has the Mazur-Ulam property (briefly MUP). As its immediateapplications, we obtain that almost-CL-spaces admitting a smoothpoint(specially, separable almost-CL-spaces) and a two-dimensional space whoseunit sphere is a hexagon has the MUP. Furthermore, we discuss the stability ofthe spaces having the MUP by the $c_0$- and $\ell_1$-sums, and show that thespace $C(K,X)$ 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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机译：我们介绍（T）属性，并证明每个具有（T）属性的Banach空间都具有Mazur-Ulam属性（简称MUP）。作为其直接应用，我们获得允许光滑点的几乎CL空间（特别是可分离的几乎CL空间）和单位球面为六边形的二维空间具有MUP。此外，我们通过$ c_0 $-和$ \ ell_1 $ -sum讨论具有MUP的空间的稳定性，并证明向量值连续函数的空间$ C（K，X）$具有MUP，其中$ X $是可分离的几乎CL的空间，$ K $是紧凑的度量空间。
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