Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Berberian extension and its S-spectra in a quaternionic Hilbert space   For a bounded right linear operators $A$, in a right quaternionic Hilbert
space $V_{\mathbb{H}}^{R}$, following the complex formalism, we study the
Berberian extension $A^\circ$, which is an extension of $A$ in a right
quaternionic Hilbert space obtained from $V_{\mathbb{H}}^{R}$. In the complex
setting, the important feature of the Berberian extension is that it converts
approximate point spectrum of $A$ into point spectrum of $A^\circ$. We show
that the same is true for the quaternionic S-spectrum. As in the complex case,
we use the Berberian extension to study some properties of the commutator of
two quaternionic bounded right linear operators.

25
The categories of this paper are: patt-sol
28
The categories of this paper are: alg-geom
14
The categories of this paper are: math-ph
26
The categories of this paper are: bayes-an
36
The categories of this paper are: cmp-lg
18
The categories of this paper are: econ
3
The categories of this paper are: physics
8
The categories of this paper are: hep-ex
17
The categories of this paper are: q-fin
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The categories of this paper are: atom-ph
10
The categories of this paper are: q-bio
11
The categories of this paper are: hep-lat
31
The categories of this paper are: ao-sci
35
The categories of this paper are: mtrl-th
30
The categories of this paper are: q-alg
22
The categories of this paper are: chao-dyn