An example of weakly amenable and character amenable operator

Details An example of weakly amenable and character amenable operator An example of weakly amenable and character amenable operator

2010-08-31

arxiv.org/abs/1008.5241v1

Mathematics

Functional Analysis

6 pages

Scientific paper

A complete characterization of Hilbert space operators that generate weakly amenable algebras remains open, even in the case of compact operator. Farenick, Forrest and Marcoux proposed the question that if $T$ is a compact weakly amenable operator on a Hilbert space $\mathfrak{H}$, then is $T$ similar to a normal operator? In this paper we demonstrate an example of compact triangular operator on infinite-dimension Hilbert space which is a weakly amenable and character amenable operator but is not similar to a normal operator.

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