Journal of Noncommutative Geometry
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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) 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