On regularities and Fredholm theory
We investigate the relationship between the regularities and the Fredholm theory in a Banach algebra.
A note on the singular spectrum.
We compare the singular spectrum of a Banach algebra element with the usual spectrum and exponential spectrum.
Rank and the Drazin inverse in Banach algebras
Let A be an arbitrary, unital and semisimple Banach algebra with nonzero socle. We investigate the relationship between the spectral rank (defined by B. Aupetit and H. Mouton) and the Drazin index for elements belonging to the socle of A. In particular, we show that the results for the finite-dimensional case can be extended to the (infinite-dimensional) socle of A.
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