Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Generalized Drazin-Riesz invertible elements in a semi-simple Banach
  algebra   We extend the notion of generalized Drazin-Riesz inverse introduced for
bounded linear operators in \cite{Ziv} to elements in a complex unital
semi-simple Banach algebra. Several characterizations and properties of
generalized Drazin-Riesz invertible elements are given. In particular, we
extend those of \cite{AbZg1,Djor,Ziv}.

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The categories of this paper are: physics
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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: patt-sol
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The categories of this paper are: atom-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: dg-ga
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The categories of this paper are: astro-ph
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The categories of this paper are: eess
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The categories of this paper are: hep-lat
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The categories of this paper are: plasm-ph
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The categories of this paper are: hep-th
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The categories of this paper are: cs
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The categories of this paper are: nlin
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The categories of this paper are: solv-int
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The categories of this paper are: bayes-an