The analysis group works in a variety of areas of classical and functional analysis. Dr J F Feinstein Banach function algebras are complete normed algebras of bounded, continuous, complex-valued functions defined on topological spaces.
T here are very many different examples with a huge variety of properties.
Two contrasting examples are the algebra of all continuous complex-valued functions on the closed unit disc, and the subalgebra of this algebra consisting of those functions which are continuous on the closed disc and analytic on the interior of the disc. In the second of these algebras, any function which is zero throughout some non-empty open set must be constantly zero. Most Banach function algebras have some features in common with one or the other of these two algebras. The aim of this project is to investigate a variety of conditions, especially regularity conditions, for Banach function algebras, and to relate these conditions to each other, and to other important conditions that Banach function algebras may satisfy. Regularity conditions have important applications in several areas of functional analysis, including automatic continuity theory and the theory of Wedderburn decompositions.