On applicability of the projection method to two-dimensional Toeplitz operators with measurable symbol.
We characterize elements in a semisimple Banach algebra which are quasinilpotent equivalent to maximal finite rank elements.
We give a spectral characterisation of rank one elements and of the socle of a semisimple Banach algebra.
Without the "scarcity lemma", two kinds of "rank one elements" are identified in semisimple Banach algebras.
We investigate the relationship between the regularities and the Fredholm theory in a Banach algebra.
In this paper we prove that the image of a nth order derivation on real commutative Banach ℓ-algebras with positive squares is contained in the set of nilpotent elements.