Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Infinite-dimensional Log-Determinant divergences between positive
  definite Hilbert-Schmidt operators   The current work generalizes the author's previous work on the
infinite-dimensional Alpha Log-Determinant (Log-Det) divergences and Alpha-Beta
Log-Det divergences, defined on the set of positive definite unitized trace
class operators on a Hilbert space, to the entire Hilbert manifold of positive
definite unitized Hilbert-Schmidt operators. This generalization is carried out
via the introduction of the extended Hilbert-Carleman determinant for unitized
Hilbert-Schmidt operators, in addition to the previously introduced extended
Fredholm determinant for unitized trace class operators. The resulting
parametrized family of Alpha-Beta Log-Det divergences is general and contains
many divergences between positive definite unitized Hilbert-Schmidt operators
as special cases, including the infinite-dimensional affine-invariant
Riemannian distance and the infinite-dimensional generalization of the
symmetric Stein divergence.

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The categories of this paper are: astro-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: cs
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The categories of this paper are: acc-phys
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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: physics
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The categories of this paper are: nucl-ex
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The categories of this paper are: cmp-lg
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The categories of this paper are: quant-ph
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The categories of this paper are: solv-int
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The categories of this paper are: gr-qc
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The categories of this paper are: chao-dyn
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The categories of this paper are: comp-gas
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The categories of this paper are: mtrl-th
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The categories of this paper are: econ