Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Strongly irreducible factorization of quaternionic operators and Riesz
  decomposition theorem   Let $T$ be a bounded quaternionic normal operator on a right quaternionic
Hilbert space $\mathcal{H}$. We show that $T$ can be factorized in a strongly
irreducible sense, that is, for any $\delta >0$ there exist a compact operator
$K$ with $\|K\|< \delta$, a partial isometry $W$ and a strongly irreducible
operator $S$ on $\mathcal{H}$ such that \begin{equation*} T = (W+K) S.
\end{equation*} We illustrate our result with an example. We also prove a
quaternionic version of the Riesz decomposition theorem and as a consequence,
show that if the spherical spectrum of a bounded quaternionic operator (need
not be normal) is disconnected by a pair of disjoint axially symmetric closed
subsets, then it is strongly reducible.

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The categories of this paper are: q-fin
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The categories of this paper are: patt-sol
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The categories of this paper are: math-ph
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The categories of this paper are: eess
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The categories of this paper are: hep-ex
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The categories of this paper are: gr-qc
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The categories of this paper are: physics
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The categories of this paper are: bayes-an
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The categories of this paper are: comp-gas
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The categories of this paper are: acc-phys
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The categories of this paper are: cmp-lg
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The categories of this paper are: nucl-ex
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The categories of this paper are: stat
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The categories of this paper are: funct-an
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The categories of this paper are: solv-int
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The categories of this paper are: supr-con