Asymptotic sequence algebras, and ultrapowers, of Banach algebras

25/10/2019, 14:00 - 15:00 in MAP/0G/017

Daws, Matthew (University of Central Lancashire)


Abstract:

We will explore the notion of the Asymptotic sequence algebra, or more generally an ultraproduct, of Banach algebras. Such objects have recently been intensively studied for C*-algebras, but have existed as objects of interest for many years now. We shall indicate links with continuous model theory. Our principle interest is in how various notions of “ring theoretic infiniteness” pass to the sequence algebra or ultraproduct. Here questions of boundedness become important, and from this we find a difference between C*-algebras and general Banach algebras; for the latter we construct counter-examples. This is joint work with Bence Horvath.

Mathematical Sciences Research Centre