About the transitivity of the property of being Segal topological algebra
Ponente(s): Mart Abel -
A topological algebra A is a left (right or two-sided) Segal topological algebra in a topological algebra B if there exists a continuous algebra homomorphism f:A\to B such that f(A) is a dense left (respectively, a right or a two-sided) ideal of B. In this case we will represent Segal topological algebra as a triple (A, f, B). In several talks about Segal topological algebras, the following question has been asked:
Let (A, f, B) and (B, g, C) be two left (right or two-sided) Segal topological algebras. Is (A, g\circ f, C) always a left (right or two-sided) Segal topological algebra, i.e., is the property of being Segal topological algebra transitive?
In the present talk we present some sufficient conditions on topological algebras in order to answer the question affirmatively. Up to now, no counter-examples are known, but the question remains still open in general.