Generalized Browder's theorem and SVEP

Pietro Aiena, Orlando Garcia

    Risultato della ricerca: Article

    16 Citazioni (Scopus)

    Abstract

    A bounded operator T∈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 H0(λI − T) as λ belongs to certain subsets of C. In the last part we give a general framework for which generalized Weyl’s theorem follows for several classes of operators
    Lingua originaleEnglish
    pagine (da-a)215-228
    Numero di pagine14
    RivistaMediterranean Journal of Mathematics
    Volume4
    Stato di pubblicazionePublished - 2007

    All Science Journal Classification (ASJC) codes

    • Mathematics(all)

    Cita questo

    Generalized Browder's theorem and SVEP. / Aiena, Pietro; Garcia, Orlando.

    In: Mediterranean Journal of Mathematics, Vol. 4, 2007, pag. 215-228.

    Risultato della ricerca: Article

    Aiena, Pietro ; Garcia, Orlando. / Generalized Browder's theorem and SVEP. In: Mediterranean Journal of Mathematics. 2007 ; Vol. 4. pagg. 215-228.
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    AB - A bounded operator T∈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 H0(λI − T) as λ belongs to certain subsets of C. In the last part we give a general framework for which generalized Weyl’s theorem follows for several classes of operators

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