Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Mazur-Ulam property for commutative von Neumann algebras   Let $(\Omega,\mu)$ be a $\sigma$-finite measure space. Given a Banach space
$X$, let the symbol $S(X)$ stand for the unit sphere of $X$. We prove that the
space $L^{\infty} (\Omega,\mu)$ of all complex-valued measurable essentially
bounded functions equipped with the essential supremum norm, satisfies the
Mazur-Ulam property, that is, if $X$ is any complex Banach space, every
surjective isometry $\Delta: S(L^{\infty} (\Omega,\mu))\to S(X)$ admits an
extension to a surjective real linear isometry $T: L^{\infty} (\Omega,\mu)\to
X$. This conclusion is derived from a more general statement which assures that
every surjective isometry $\Delta : S(C(K))\to S(X),$ where $K$ is a Stonean
space, admits an extension to a surjective real linear isometry from $C(K)$
onto $X$.

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The categories of this paper are: cond-mat
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The categories of this paper are: solv-int
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The categories of this paper are: hep-lat
32
The categories of this paper are: atom-ph
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The categories of this paper are: hep-ph
21
The categories of this paper are: adap-org
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The categories of this paper are: alg-geom
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The categories of this paper are: nlin
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The categories of this paper are: nucl-th
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The categories of this paper are: funct-an
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The categories of this paper are: econ
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The categories of this paper are: ao-sci
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The categories of this paper are: nucl-ex
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The categories of this paper are: gr-qc
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The categories of this paper are: mtrl-th
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The categories of this paper are: stat