Weyl type theorems for p-hyponormal and M-hyponormal operators

• Autorzy: Xiaohong Cao , Maozheng Guo , Bin Meng
• Języki publikacji: EN

Abstrakty

EN

"Generalized Weyl's theorem holds" for an operator when the complement in the spectrum of the B-Weyl spectrum coincides with the isolated points of the spectrum which are eigenvalues; and "generalized a-Weyl's theorem holds" for an operator when the complement in the approximate point spectrum of the semi-B-essential approximate point spectrum coincides with the isolated points of the approximate point spectrum which are eigenvalues. If T or T* is p-hyponormal or M-hyponormal then for every f ∈ H(σ(T)), generalized Weyl's theorem holds for f(T), so Weyl's theorem holds for f(T), where H(σ(T)) denotes the set of all analytic functions on an open neighborhood of σ(T). Moreover, if T* is p-hyponormal or M-hyponormal then for every f ∈ H(σ(T)), generalized a-Weyl's theorem holds for f(T) and hence a-Weyl's theorem holds for f(T).

Kategorie tematyczne

• 47A53: (Semi-) Fredholm operators; index theories
• 47A55: Perturbation theory
• 47A10: Spectrum, resolvent

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Studia Mathematica
• Rocznik: 2004
• Tom: 163
• Numer: 2
• Strony: 177-188

Daty

wydano

2004

Twórcy

autor

Xiaohong Cao

• College of Mathematics and, Information Science, Shaanxi Normal University, Xi'an, 710062, P.R. China

autor

Maozheng Guo

• LMAM, School of Mathematical Sciences, Peking University, Beijing, 100871, P.R. China

autor

Bin Meng

• LMAM, School of Mathematical Sciences, Peking University, Beijing, 100871, P.R. China

Identyfikatory

DOI

10.4064/sm163-2-5