Weyl's theorem for algebraically k-quasiclass a operators

• Autorzy: Gao F. , Fang X.
• Języki publikacji: EN

Abstrakty

EN

If T or T* is an algebraically k-quasiclass A operator acting on an infinite dimensional separable Hilbert space and F is an operator commuting with T, and there exists a positive integer n such that Fn has a finite rank, then we prove that Weyl's theorem holds for ∫ (T)+F for every ∫∈ H(σ (T)), where H(σ (T)) denotes the set of all analytic functions in a neighborhood of σ (T). Moreover, if T* is an algebraically k-quasiclass A operator, then α-Weyl's theorem holds for ∫(T). Also, we prove that if T or T* is an algebraically k-quasiclass A operator then both the Weyl spectrum and the approximate point spectrum of T obey the spectral mapping theorem for every ∫∈ H(σ (T)).

Słowa kluczowe

EN

algebraically k-quasiclass A operator; Weyl's theorem; alpha-Weyl's theorem

• Wydawca: AGH University of Science and Technology Press
• Czasopismo: Opuscula Mathematica
• Rocznik: 2012
• Tom: Vol. 32, no. 1
• Strony: 125--135
• Opis fizyczny: Bibliogr. 32 poz.

Twórcy

autor

Gao F.

autor

Fang X.

• Henan Normal University College of Mathematics and Information Science Xinxiang, Henan 453007, China,

Bibliografia

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