Abstract

The focus of this thesis is the study of the properties of the maximal ideal space of a sequence algebra of continuous functions. The results obtained concern both the topological and the analytic structure of this space. It turns out that the structure of the maximal ideal space of such an algebra resembles the structure of the maximal ideal space of H ^∞. As one can expect, this parallelism goes further when the sequence algebra of continuous functions is [special characters omitted], the algebra of bounded sequences of functions belonging to the disc algebra [special characters omitted]. Given this parallelism; the tool that we used is the fibering of the maximal ideal space of the sequence algebra. For the particular case of [special characters omitted] we combined this with the use of the properties of sequences of finite Blaschke products. In this manner, we obtained results concerning the size of these fibers and their connectedness in the general case, as well as a description of the analytic structure of the maximal ideal space of [special characters omitted].