This paper is devoted to the investigation of Weyl and essential S-spectra a bounded right quaternionic linear operator in Hilbert space. Using Riesz projection, S-eigenvalue finite type both introduced studied. In particular, we have shown that do not contain eigenvalues type. We also described boundary S-spectrum particular case spectral theorem S-spectrum.

This work contains a constructive example of a class of Jacobi operators with an arbitrary finite number of gaps in its unbounded essential spectrum. The construction of this class is based on elementary ideas of gluing finite-dimensional Jacobi matrices whose sizes grow to infinity. The precise analysis of the finite-dimensional pieces leads to a new “finite essential spectrum” besides the nat...

in this paper‎, ‎we show the stability of gustafson‎, ‎weidmann‎, ‎kato‎, ‎wolf‎, ‎schechter and browder essential spectrum of bounded linear operators on banach spaces which remain invariant under additive perturbations‎ ‎belonging to a broad classes of operators $u$ such $gamma(u^m)