Almost normal operators mod Hilbert–Schmidt and the $K$-theory of the algebras $E\Lambda (\Omega )$

Abstract

Is there a mod Hilbert–Schmidt analogue of the BDF-theorem, with the Pincus $g$-function playing the role of the index? We show that part of the question is about the $K$-theory of certain Banach algebras. These Banach algebras, related to Lipschitz functions and Dirichlet algebras have nice Banach-space duality properties. Moreover their corona algebras are $C\ast$-algebras.