Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: On Schatten restricted norms   We consider norms on a complex separable Hilbert space such that $\langle
a\xi,\xi\rangle\leq\|\xi\|^2\leq\langle b\xi,\xi\rangle$ for positive
invertible operators $a$ and $b$ that differ by an operator in the Schatten
class. We prove that these norms have unitarizable isometry groups, our proof
uses a generalization of a fixed point theorem for isometric actions on
positive invertible operators. As a result, if the isometry group does not
leave any finite dimensional subspace invariant, then the norm must be
Hilbertian. That is, if a Hilbertian norm is changed to a close non-Hilbertian
norm, then the isometry group does leave a finite dimensional subspace
invariant. The approach involves metric geometric arguments related to the
canonical action of the group on the non-positively curved space of positive
invertible Schatten perturbations of the identity .

15
The categories of this paper are: nucl-ex
27
The categories of this paper are: comp-gas
12
The categories of this paper are: nucl-th
28
The categories of this paper are: alg-geom
6
The categories of this paper are: astro-ph
1
The categories of this paper are: cs
32
The categories of this paper are: atom-ph
31
The categories of this paper are: ao-sci
25
The categories of this paper are: patt-sol
22
The categories of this paper are: chao-dyn
11
The categories of this paper are: hep-lat
33
The categories of this paper are: plasm-ph
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The categories of this paper are: eess
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The categories of this paper are: stat
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The categories of this paper are: mtrl-th
7
The categories of this paper are: hep-th