Illinois Journal of Mathematics

An example of weakly amenable and character amenable operator

Luo Yi Shi and You Qing Ji

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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.

Article information

Source
Illinois J. Math., Volume 55, Number 4 (2011), 1415-1422.

Dates
First available in Project Euclid: 12 July 2013

Permanent link to this document
https://projecteuclid.org/euclid.ijm/1373636690

Digital Object Identifier
doi:10.1215/ijm/1373636690

Mathematical Reviews number (MathSciNet)
MR3082875

Zentralblatt MATH identifier
1270.47037

Subjects
Primary: 47C05: Operators in algebras
Secondary: 46H35: Topological algebras of operators [See mainly 47Lxx] 47A65: Structure theory 47A66: Quasitriangular and nonquasitriangular, quasidiagonal and nonquasidiagonal operators 47B15: Hermitian and normal operators (spectral measures, functional calculus, etc.)

Citation

Shi, Luo Yi; Ji, You Qing. An example of weakly amenable and character amenable operator. Illinois J. Math. 55 (2011), no. 4, 1415--1422. doi:10.1215/ijm/1373636690. https://projecteuclid.org/euclid.ijm/1373636690


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