Abstract:
In a right quaternionic Hilbert space, for a bounded right lin ear operator, the Kato S-spectrum is introduced and studied to certain
extent. In particular, it is shown that the Kato S-spectrum is a non empty compact subset of the S-spectrum and it contains the boundary
of the S-spectrum. Using right-slice regular functions, local S-spectrum,
at a point of a right quaternionic Hilbert space, and the local spectral
subsets are introduced and studied. The S-surjectivity spectrum and its
connections to the Kato S-spectrum, approximate S-point spectrum and
local S-spectrum are investigated. The generalized Kato S-spectrum is
introduced and it is shown that the generalized Kato S-spectrum is a
compact subset of the S-spectrum.
