Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Improvement on a Generalized Lieb's Concavity Theorem   We show that Lieb's concavity theorem holds more generally for any unitary
invariant matrix function $\phi:\mathbf{H}_+^n\rightarrow \mathbb{R}_+^n$ that
is concave and satisfies H\"older's inequality. Concretely, we prove the joint
concavity of the function $(A,B)
\mapsto\phi\big[(B^\frac{qs}{2}K^*A^{ps}KB^\frac{qs}{2})^{\frac{1}{s}}\big] $
on $\mathbf{H}_+^n\times\mathbf{H}_+^m$, for any $K\in \mathbb{C}^{n\times m}$
and any $s,p,q\in(0,1], p+q\leq 1$. This result improves a recent work by Huang
for a more specific class of $\phi$.

29
The categories of this paper are: funct-an
14
The categories of this paper are: math-ph
17
The categories of this paper are: q-fin
11
The categories of this paper are: hep-lat
21
The categories of this paper are: adap-org
12
The categories of this paper are: nucl-th
25
The categories of this paper are: patt-sol
32
The categories of this paper are: atom-ph
0
The categories of this paper are: hep-ph
33
The categories of this paper are: plasm-ph
37
The categories of this paper are: supr-con
34
The categories of this paper are: chem-ph
16
The categories of this paper are: stat
27
The categories of this paper are: comp-gas
36
The categories of this paper are: cmp-lg
13
The categories of this paper are: quant-ph