Abstract
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)*.
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The research was supported by the International Cooperation Project between the University of Palermo (Italy) and Conicit-Venezuela.
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Aiena, P., Biondi, M.T. Some spectral mapping theorems through local spectral theory. Rend. Circ. Mat. Palermo 53, 165–184 (2004). https://doi.org/10.1007/BF02872869
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DOI: https://doi.org/10.1007/BF02872869