Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Generalized-Lush Spaces and the Mazur-Ulam Property   We introduce a new class of Banach spaces, called generalized-lush spaces
(GL-spaces for short), which contains almost-CL-spaces, separable lush spaces
(specially, separable $C$-rich subspaces of $C(K)$), and even the
two-dimensional space with hexagonal norm. We obtain that the space $C(K,E)$ of
the vector-valued continuous functions is a GL-space whenever $E$ is, and show
that the GL-space is stable under $c_0$-, $l_1$- and $l_\infty$-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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The categories of this paper are: cmp-lg
8
The categories of this paper are: hep-ex
14
The categories of this paper are: math-ph
12
The categories of this paper are: nucl-th
3
The categories of this paper are: physics
34
The categories of this paper are: chem-ph
7
The categories of this paper are: hep-th
27
The categories of this paper are: comp-gas
21
The categories of this paper are: adap-org
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The categories of this paper are: ao-sci
9
The categories of this paper are: nlin
26
The categories of this paper are: bayes-an
20
The categories of this paper are: acc-phys
10
The categories of this paper are: q-bio
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The categories of this paper are: alg-geom
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The categories of this paper are: q-fin