Weyl’s Theorem for Algebraically Quasi-class A Operators
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If T or T* is an algebraically quasi-class A operator acting on an infinite dimensional separable Hilbert space then we prove that Weyl’s theorem holds for f(T) for every f ∈ H(σ(T)), where H(σ(T)) denotes the set of all analytic functions in an open neighborhood of σ(T). Moreover, if T* is algebraically quasi-class A then a-Weyl’s theorem holds for f(T). Also, if T or T* is an algebraically quasi-class A operator then we establish that the spectral mapping theorems for the Weyl spectrum and the essential approximate point spectrum of T for every f ∈ H(σ(T)), respectively.
Keywords.Weyl’s theorem Browder’s theorem algebraically quasi-class A operator a-Weyl’s theorem a-Browder’s theorem single valued extension property
Mathematics Subject Classification (2000).Primary 47A10, 47A53 Secondary 47B20
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