Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Logarithmic submajorisation and order-preserving linear isometries   Let $\mathcal{E}$ and $\mathcal{F}$ be symmetrically $\Delta$-normed (in
particular, quasi-normed) operator spaces affiliated with semifinite von
Neumann algebras $\mathcal{M}_1$ and $\mathcal{M}_2$, respectively. We
establish a noncommutative version of Abramovich's theorem \cite{A1983}, which
provides the general form of normal order-preserving linear operators
$T:\mathcal{E} \stackrel{into}{\longrightarrow} \mathcal{F}$ having the
disjointness preserving property. As an application, we obtain a noncommutative
Huijsmans-Wickstead theorem \cite{Huijsmans_W}. By establishing the
disjointness preserving property for an order-preserving isometry
$T:\mathcal{E} \stackrel{into}{\longrightarrow} \mathcal{F}$, we obtain the
existence of a Jordan $*$-monomorphism from $\mathcal{M}_1$ into
$\mathcal{M}_2$ and the general form of this isometry, which extends and
complements a number of existing results. In particular, we fully resolve the
case when $\mathcal{F}$ is the predual of $\mathcal{M}_2$ and other untreated
cases in [Sukochev-Veksler, IEOT, 2018].

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The categories of this paper are: hep-ex
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The categories of this paper are: chao-dyn
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The categories of this paper are: comp-gas
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The categories of this paper are: nucl-th
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The categories of this paper are: stat
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The categories of this paper are: acc-phys
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The categories of this paper are: hep-th
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The categories of this paper are: hep-lat
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The categories of this paper are: astro-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: ao-sci
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The categories of this paper are: plasm-ph
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The categories of this paper are: nlin
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The categories of this paper are: bayes-an
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The categories of this paper are: patt-sol
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The categories of this paper are: solv-int