Almost normal operators mod Hilbert-Schmidt and the K-theory of the   Banach algebras $E\Lambda(\Omega)$
  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*-algebras. 
Dan-Virgil Voiculescu
math.OA math.SP