Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Some loose ends on eventual domination and positivity   We consider two $C_0$-semigroups $(e^{tA})_{t \ge 0}$ and $(e^{tB})_{t \ge
0}$ on function spaces (or, more generally, on Banach lattices) and analyse
eventual domination between them in the sense that $\lvert e^{tA}f \rvert \le
e^{tB} \lvert f \rvert$ for all sufficiently large times $t$. We characterise
this behaviour and prove a number of theoretical results which complement
earlier results given by Mugnolo and the second author in the special case
where both semigroups are positive for large times.
  Moreover, we study the analogous question of whether the resolvent of $B$
eventually dominates the resolvent of $A$ close to the spectral bound of $B$.
This is closely related to the so-called maximum and anti-maximum principles.
In order to demonstrate how our results can be used, we include several
applications to concrete differential operators.
  At the end of the paper, we demonstrate that the eventual positivity of the
resolvent of an operator is closely related to the eventual positivity of the
Ces\`aro means of the generated semigroup.

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The categories of this paper are: chem-ph
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The categories of this paper are: cs
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The categories of this paper are: math-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: hep-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: quant-ph
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The categories of this paper are: acc-phys
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The categories of this paper are: adap-org
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The categories of this paper are: funct-an
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The categories of this paper are: hep-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: comp-gas
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The categories of this paper are: nlin