2018/11/06 by Jared T. White, White, Jared T.
Mathematics · #Advanced Banach Space Theory #Advanced Operator Algebra Research #Advanced Topics in Algebra
paper · pdf · doi:10.48550/arxiv.1811.02393
We investigate topologically left Noetherian Banach algebras. We show that if G is a compact group, then L 1(G) is topologically left Noetherian if and only if G is metrisable. We prove that, given a Banach space E such that E' has BAP, the algebra of compact operators K(E) is topologically left Noetherian if and only if E' is separable; it is topologically right Noetherian if and only if E is separable. We then give some examples of dual Banach algebras which are topologically left Noetherian in the weak*-topology. Finally we give a unified approach to classifying the weak*-closed left ideals of certain dual Banach algebras that are also multiplier algebras, with applications to M(G) for G a compact group, and B(E) for E a reflexive Banach space with AP.