Abstract:

The sufficient and necessary conditions are given for an operational calculus which satisfies a-Browder theorem and has property  (ω₁)  by the variant of the essential approximate point spectrum σ₁(·) and the spectrum σ₂(·) defined in terms of the property of consistency in invertibility. Then the relation is considered between a-Browder theorem holding for an operational calculus and its conjugate having property (ω₁). Besides, we research the condition of the operational calculus of an H(P) operator having property (ω₁).

Key words:  spectrum; a-Browder theorem; property (ω₁)