Some spectral mapping theorems through local spectral theory

  • Pietro Aiena
  • Maria Teresa Biondi


The spectral mapping theorems for Browder spectrum and for semi-Browder spectra have been proved by several authors [14], [29] and [33], by using different methods. We shall employ a local spectral argument to establish these spectral mapping theorems, as well as, the spectral mapping theorem relative to some other classical spectra.

We also prove that ifT orT* has the single-valued extension property some of the more important spectra originating from Fredholm theory coincide. This result is extended, always in the caseT orT* has the single valued extension property, tof(T), wheref is an analytic function defined on an open disc containing the spectrum ofT. In the last part we improve a recent result of Curto and Han [10] by proving that for every transaloid operatorT a-Weyl’s theorem holds forf(T) andf(T)*.

1991 Mathematics Reviews

Primary 47A10 47A11, 47A53 Secondary 47A15, 47B20 

Key words and phrases

Single valued extension property Weyl and semi-Browder operators spectral mapping theorems Weyl’s theorem 


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Copyright information

© Springer 2004

Authors and Affiliations

  • Pietro Aiena
    • 1
  • Maria Teresa Biondi
    • 2
  1. 1.Dipartimento di Matematica ed Applicazioni Facoltà di IngegneriaUniversità di PalermoPalermoItaly
  2. 2.Departmento de Matemáticas, Facultad de CienciasUniversidad UCLA de BarquisimetoVenezuela

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