Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Operator revision of a Ky Fan type inequality   Let $\mathscr{H}$ be a complex Hilbert space and $A,B\in
\mathbb{B}(\mathscr{H})$ such that $0<A,B\leq\frac{1}{2}I$. Setting $A':=I-A$
and $B':=I-B$, we prove $$ A'\nabla_\lambda B'-A'!_\lambda B' \leq
A\nabla_\lambda B-A!_\lambda B, $$ where $\nabla_\lambda$ and $!_\lambda$
denote the weighted arithmetic and harmonic operator means, respectively. This
inequality is the natural extension of a Ky Fan type inequality due to H.
Alzer. Some parallel and related results are also obtained.

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The categories of this paper are: adap-org
0
The categories of this paper are: hep-ph
25
The categories of this paper are: patt-sol
36
The categories of this paper are: cmp-lg
4
The categories of this paper are: cond-mat
17
The categories of this paper are: q-fin
31
The categories of this paper are: ao-sci
33
The categories of this paper are: plasm-ph
34
The categories of this paper are: chem-ph
1
The categories of this paper are: cs
37
The categories of this paper are: supr-con
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-lat
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The categories of this paper are: funct-an
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The categories of this paper are: alg-geom
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The categories of this paper are: hep-ex