Open Access
Winter 2011 An example of weakly amenable and character amenable operator
Luo Yi Shi, You Qing Ji
Illinois J. Math. 55(4): 1415-1422 (Winter 2011). DOI: 10.1215/ijm/1373636690

Abstract

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-dimensional Hilbert space which is a weakly amenable and character amenable operator but is not similar to a normal operator.

Citation

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Luo Yi Shi. You Qing Ji. "An example of weakly amenable and character amenable operator." Illinois J. Math. 55 (4) 1415 - 1422, Winter 2011. https://doi.org/10.1215/ijm/1373636690

Information

Published: Winter 2011
First available in Project Euclid: 12 July 2013

zbMATH: 1270.47037
MathSciNet: MR3082875
Digital Object Identifier: 10.1215/ijm/1373636690

Subjects:
Primary: 47C05
Secondary: 46H35 , 47A65 , 47A66 , 47B15

Rights: Copyright © 2011 University of Illinois at Urbana-Champaign

Vol.55 • No. 4 • Winter 2011
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