J4 ›› 2011, Vol. 46 ›› Issue (4): 108-112.

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The equivalence of a-Browder theorem and property (ω1) for operational calculus of operators

ZHANG He-jia, CAO Xiao-hong*   

  1. College of Mathematics and Information Science, Shaanxi Normal University, Xi′an 710062, Shaanxi, China
  • Received:2010-03-31 Published:2011-04-21


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)

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