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