Thesis submitted for the degree of Ph. D. Uniform Convergence to the Spectral Radius and Some Related Properties in Banach Algebras

Gelfand’s assertion of the equality of the spectral radius of an element a of a Banach algebra with the limit of the sequence ‖an‖1/n is ample motivation for the study of Banach algebras. In this work, whose scope is the general structure theory of Banach algebras, we investigate conditions of uniformity in this convergence