caa a22 4500 463245946 CHVBK 20180405153325.0 cr unu---uuuuu 170326e20070701xx s 000 0 eng 10.1007/s00009-007-0113-2 doi (NATIONALLICENCE)springer-10.1007/s00009-007-0113-2 Generalized Browder's Theorem and SVEP [Elektronische Daten] [Pietro Aiena, Orlando Garcia] Abstract.: A bounded operator $$T \in L(X), X$$ a Banach space, is said to verify generalized Browder's theorem if the set of all spectral points that do not belong to the B-Weyl's spectrum coincides with the set of all poles of the resolvent of T, while T is said to verify generalized Weyl's theorem if the set of all spectral points that do not belong to the B-Weyl spectrum coincides with the set of all isolated points of the spectrum which are eigenvalues. In this article we characterize the bounded linear operators T satisfying generalized Browder's theorem, or generalized Weyl's theorem, by means of localized SVEP, as well as by means of the quasi-nilpotent part H 0(λI − T) as λ belongs to certain subsets of $${\mathbb{C}}$$ . In the last part we give a general framework for which generalized Weyl's theorem follows for several classes of operators. Birkhäuser Verlag Basel/Switzerland, 2007 SVEP nationallicence Fredholm theory nationallicence generalized Weyl's theorem and generalized Browder's theorem nationallicence Aiena Pietro Dipartimento di Matematica ed Applicazioni Facoltà di Ingegneria, Università di Palermo, Viale delle Scienze, I-90128, Palermo, Italy aut Garcia Orlando Departamento de Matemáticas Facultad de Ciencias, Universidad UDO, Cumaná, Venezuela aut Mediterranean Journal of Mathematics Birkhäuser-Verlag; www.birkhäuser.ch 4/2(2007-07-01), 215-228 1660-5446 4:2<215 2007 4 9 https://doi.org/10.1007/s00009-007-0113-2 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s00009-007-0113-2 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Aiena Pietro Dipartimento di Matematica ed Applicazioni Facoltà di Ingegneria, Università di Palermo, Viale delle Scienze, I-90128, Palermo, Italy aut NATIONALLICENCE 700 1- Garcia Orlando Departamento de Matemáticas Facultad de Ciencias, Universidad UDO, Cumaná, Venezuela aut NATIONALLICENCE 773 0- Mediterranean Journal of Mathematics Birkhäuser-Verlag; www.birkhäuser.ch 4/2(2007-07-01), 215-228 1660-5446 4:2<215 2007 4 9 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer