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## Studia Mathematica

2013 | 219 | 2 | 139-153
Tytuł artykułu

### Generalized-lush spaces and the Mazur-Ulam property

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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 $l_{∞}$-sums. As an application, we prove that the Mazur-Ulam property holds for a larger class of Banach spaces, called local-GL-spaces, including all lush spaces and GL-spaces. Furthermore, we generalize the stability properties of GL-spaces to local-GL-spaces. From this, we can obtain many examples of Banach spaces having the Mazur-Ulam property.
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Numer
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139-153
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wydano
2013
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• Department of Mathematics, Tianjin University of Technology, 300384 Tianjin, China
autor
• Department of Mathematics, Tianjin University of Technology, 300384 Tianjin, China
autor
• Department of Mathematics and LPMC, Nankai University, 300071 Tianjin, China
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