Operator algebras with contractive approximate identities: Weak compactness and the spectrum

2014/07/02 by David P. Blecher, C. J. Read, Charles John Read
Mathematics · #Advanced Banach Space Theory #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebra over a field #Compact operator #Compact space #Computer science #Discrete mathematics #Mathematics #Operator (biology) #Operator algebra #Pure mathematics #Spectrum (functional analysis) #math.FA #math.OA

paper · pdf · doi:10.1016/j.jfa.2014.06.007

11 pages. To appear Journal of Functional Analysis. arXiv admin note: substantial text overlap with arXiv:1308.2723

openalex publication_date 2014/07/02 · arxiv created 2014/07/05 · arxiv updated 2014/07/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We continue our study of operator algebras with contractive approximate identities (cais) by presenting a couple of interesting examples of operator algebras with cais, which in particular answer questions raised in previous papers in this series, for example about whether, roughly speaking, `weak compactness' of an operator algebra, or the lack of it, can be seen in the spectra of its elements.

Citations

• Operator algebras with contractive approximate identities, III
• Hereditary subalgebras of operator algebras
• Ideals and structure of operator algebras