Abstract:

We gave the definition of generalized Kato type operators and defined the new spectrum in view of the property of generalized Kato o
perators. We establish the sufficient and necessary conditions for a bounded linear operator defined on a Hilbert space under which generalized property (ω) holds, and obtained the sufficient and necessary conditions for a bounded linear operator on a Hilbert space, which has generalized property (ω) under perturbations by finite rank operators and power finite rank operators.

Key words: generalized Kato type operators, generalized property (ω), perturbation