Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Lifshitz-Krein trace formula for Hirsch functiuonal calculus on Banach
  spaces   We give a simple definition of a spectral shift function for pairs of
nonpositive operators on Banach spaces and prove trace formulas of
Lifshitz-Kre\u{\i}n type for a perturbation of an operator monotonic (negative
complete Bernstein) function of negative and nonpositive operators on Banach
spaces induced by nuclear perturbation of an operator argument. The
Lipschitzness of such functions is also investigated. The results may be
regarded as a contribution to a perturbation theory for Hirsch functional
calculus.

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The categories of this paper are: dg-ga
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The categories of this paper are: alg-geom
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The categories of this paper are: chem-ph
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The categories of this paper are: funct-an
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The categories of this paper are: cmp-lg
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The categories of this paper are: nucl-th
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The categories of this paper are: patt-sol
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The categories of this paper are: hep-th
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The categories of this paper are: q-fin
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The categories of this paper are: comp-gas
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The categories of this paper are: quant-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: gr-qc
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The categories of this paper are: supr-con
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The categories of this paper are: econ
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The categories of this paper are: hep-ex