Journal of Noncommutative Geometry


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Volume 8, Issue 4, 2014, pp. 1123–1145
DOI: 10.4171/JNCG/181

Published online: 2015-02-02

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

Dan-Virgil Voiculescu[1]

(1) University of California, Berkeley, United States

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.

Keywords: Trace-class self-commutator, K-theory, Dirichlet algebras, bidual Banach algebra

Voiculescu Dan-Virgil: Almost normal operators mod Hilbert–Schmidt and the $K$-theory of the algebras $E \Lambda (\Omega)$. J. Noncommut. Geom. 8 (2014), 1123-1145. doi: 10.4171/JNCG/181