2010/08/31 by Luoyi Shi, Luo Yi Shi, Shi, Luo Yi +5
Mathematics · #47C05 #Advanced Banach Space Theory #Advanced Operator Algebra Research #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #math.FA #msc:47C05
paper · pdf · doi:10.48550/arxiv.1008.5241
6 pages
arxiv created 2010/08/31 · openalex publication_date 2010/08/31 · arxiv updated 2010/09/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 \mathfrakH, 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.