Finitely-generated maximal left ideals in Banach algebras

11/05/2012 - 4:00pm
11/05/2012 - 5:00pm
H.G. Dales, University of Lancaster, UK

I shall attack the following conjecture: Let A be a unital Banach algebra. Suppose that all maximal left ideals in A are finitely-generated. Then A is finite-dimensional.
This is true when A is a C∗-algebra, or when A is commutative, and, in the latter case, we may not need all the maximal left ideals to be finitely-generated.
Now suppose that A is the algebra B(E) of all bounded linear operators on a Banach space E. I can prove the conjecture for ‘most’, but not all, Banach spaces E.
This talk is based on two joint papers, one with Wieslaw Zelazko,one with Tomasz Kania, Tomasz Kochanek, Piotr Koszmider, and Niels Laustsen.

Roberts North 105, Claremont McKenna College
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