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RESEARCH PRODUCT
Some spectral mapping theorems through local spectral theory
Maria T. BiondiPietro Aienasubject
Pure mathematicsSpectral theoryTransform theoryGeneral MathematicsSpectrum (functional analysis)Mathematical analysisExtension (predicate logic)Single valued extension property Weyl and semi-Browder operators spectral mapping theorems Weyl’s theoremFredholm theorySpectral linesymbols.namesakesymbolsSpectral theory of ordinary differential equationsAnalytic functionMathematicsdescription
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)*.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2004-06-01 | Rendiconti del Circolo Matematico di Palermo |