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

100%

Tan D.

Bulletin of the Polish Academy of Sciences. Mathematics

2008

tom 56

nr 3

225-230

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

51%

Tan D., Huang X., Liu R.

Studia Mathematica

2013

tom 219

nr 2

139-153

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.

Ograniczanie wyników

1 Bulletin of the Polish Academy of Sciences. Mathematics

1 Studia Mathematica

2 Tan D.

1 Huang X.

1 Liu R.

1 2013

1 2008

Wyniki wyszukiwania

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

Generalized-lush spaces and the Mazur-Ulam property