Journal of Operator Theory

Volume 34, Issue 2, Fall 1995 pp. 239-249.

When the algebra generated by an operator is amenable

Authors: G.A. Willis
Author institution:Department of Mathematics, University of Newcastle, University Drive, Callaghan, New South Wales, 2308, AUSTRALIA

Summary: It is shown that, if the algebra generated by a compact operator on Hilbert space is amenable, then the operator is similar to a normal operator. Problems arise with attempts to extend this to Banach spaces other than Hilbert space, for example it cannot even be shown that the operator is not quasinilpotent. The approximation property appears to be implicated in these problems.

Keywords: Amenable, compact operator, normal operator, approximation property.

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