  In a right quaternionic Hilbert space, for a bounded right linear operator,
the Kato S-spectrum is introduced and studied to a 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.
