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On Maps which Preserve Equality of Distance in F*-spaces

Dongni Tan — 2008

Bulletin of the Polish Academy of Sciences. Mathematics

We prove that every map T between two F*-spaces which preserves equality of distance and satisfies T(0) = 0 is linear.

Generalized-lush spaces and the Mazur-Ulam property

Dongni Tan; Xujian Huang; Rui Liu — 2013

Studia Mathematica

We introduce a new class of Banach spaces, called generalized-lush spaces (GL-spaces for short), which contains almost-CL-spaces, separable lush spaces (in particular, separable C-rich subspaces of C(K)), and even the two-dimensional space with hexagonal norm. We find that the space C(K,E) of vector-valued continuous functions is a GL-space whenever E is, and show that the set of GL-spaces is stable under c₀-, l₁- and $l_{\infty}$ -sums. As an application, we prove that the Mazur-Ulam property holds for a larger...

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