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# Wydawnictwa / Czasopisma IMPAN / Studia Mathematica / Wszystkie zeszyty

## Generalized Weyl's theorem and quasi-affinity

### Tom 198 / 2010

Studia Mathematica 198 (2010), 105-120 MSC: Primary 47A11, 47A53; Secondary 47A10. DOI: 10.4064/sm198-2-1

#### Streszczenie

A bounded operator $T\in L(X)$ acting on a Banach space $X$ is said to satisfy generalized Weyl's theorem if the complement in the spectrum of the B-Weyl spectrum is the set of all eigenvalues which are isolated points of the spectrum. We prove that generalized Weyl's theorem holds for several classes of operators, extending previous results of Istrăţescu and Curto–Han. We also consider the preservation of generalized Weyl's theorem between two operators $T\in L(X)$, $S\in L(Y)$ intertwined or asymptotically intertwined by a quasi-affinity $A\in L(X,Y)$.

#### Autorzy

• Pietro AienaDipartimento di Metodi e Modelli Matematici
Facoltà di Ingegneria
Università di Palermo
Viale delle Scienze
I-90128 Palermo, Italy
e-mail
• Mohammed BerkaniDépartement de Mathématiques
Faculté des Sciences
Université Mohammed I
Oujda, Morocco
e-mail

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