Abstract:

The definition of the generalized Kato type is given.  New spectra are defined in view of the generalized Kato property and the property of consistence in Fredholm and index.  The sufficient and necessary conditions  are established for a bounded linear operator defined on a Hilbert space for which the generalized property (ω′) holds. Also, the stability of a generalized property (ω′) is discussed. In addition, as a consequence of the main result, the generalized property (ω′) and its perturbation for H(p) operators are studied.

Key words: generalized Kato type; generalized property (ω′); consistent Fredholm and index operators; perturbation