Abstract: 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.
Abstract: In this paper, we discuss some properties of left
spectrum and give the representation of linear preserver map the left
spectrum of diagonal quaternionic matrices.