Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: In-betweenness: a geometric monotonicity property for operator means   We introduce the notions of in-betweenness and monotonicity with respect to a
metric, for operator means. These notions can be seen as generalising their
natural counterpart for scalar means, and as a relaxation of the notion of
geodesity. We exhibit two classes of non-trivial means that are monotonic with
respect to the Euclidean metric. We also show that all Kubo-Ando means are
monotonic with respect to the trace metric, which is the natural metric for the
geometric mean.

15
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: nucl-th
0
The categories of this paper are: hep-ph
5
The categories of this paper are: gr-qc
21
The categories of this paper are: adap-org
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The categories of this paper are: mtrl-th
31
The categories of this paper are: ao-sci
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The categories of this paper are: chao-dyn
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The categories of this paper are: funct-an
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-lat
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The categories of this paper are: q-alg
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The categories of this paper are: hep-ex
6
The categories of this paper are: astro-ph