Extensions of uniform algebras and projections
Sam Morley (University of Nottingham)
Tuesday 22nd November, 2016 16:00-17:00 Maths 522
In his thesis, Cole constructed a counter-example to the peak point conjecture by constructing various extensions of a certain uniform algebra. One of the key ingredients of his construction is the existence of a contractive, unital linear map from the extension to the original algebra which satisfies certain properties. This linear map is used to prove that these extensions are non-trivial - that is, it is not equal to the corresponding C(K) space - if the original algebra was non-trivial, along with various other properties. In this talk, we discuss generalisations of Cole’s constructions. We consider those uniform algebras which admit a contractive, unital projection whose range is a subalgebra, and the connection with some results from operator algebras.