Spherical Spectrum Properties of Quaternionic Operators

In this paper, the similarity invariant and the upper
semi-continuity of spherical spectrum, and the spherical spectrum
properties for infinite direct sums of quaternionic operators are
characterized, respectively. As an application of some results
established, a concrete example about the computation of the
spherical spectrum of a compact quaternionic operator with form of
infinite direct sums of quaternionic matrices is also given.

Authors:

• Yiwan Guo
• Fahui Zhai

Keywords:

• Spherical spectrum
• Quaternionic operator
• Upper semi-continuity
• Direct sum of operators.

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