Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On the Araki-Lieb-Thirring inequality   We prove an inequality that complements the famous Araki-Lieb-Thirring (ALT)
inequality for positive matrices $A$ and $B$, by giving a lower bound on the
quantity $\trace[A^r B^r A^r]^q$ in terms of $\trace[ABA]^{rq}$ for $0\le r\le
1$ and $q\ge0$, whereas the ALT inequality gives an upper bound. The bound
contains certain norms of $A$ and $B$ as additional ingredients and is
therefore of a different nature than the Kantorovich type inequality obtained
by Bourin (\textit{Math. Inequal. Appl.} \textbf{8}(2005) pp. 373--378) and
others. Secondly, we also prove a generalisation of the ALT inequality to
general matrices.

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The categories of this paper are: nucl-ex
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The categories of this paper are: gr-qc
10
The categories of this paper are: q-bio
35
The categories of this paper are: mtrl-th
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The categories of this paper are: supr-con
34
The categories of this paper are: chem-ph
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The categories of this paper are: eess
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The categories of this paper are: hep-lat
6
The categories of this paper are: astro-ph
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The categories of this paper are: solv-int
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The categories of this paper are: econ
27
The categories of this paper are: comp-gas
14
The categories of this paper are: math-ph
33
The categories of this paper are: plasm-ph
28
The categories of this paper are: alg-geom
0
The categories of this paper are: hep-ph