2013/08/13 by David P. Blecher, Blecher, David P., C. J. Read +2 · 2 citations
Mathematics · Physics and Astronomy · #Advanced Banach Space Theory #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Mathematical Physics (math-ph) #Operator Algebras (math.OA) #math-ph #math.FA #math.MP #math.OA
paper · pdf · doi:10.48550/arxiv.1308.2723
28 pages--several corrections made (nearly all being typos)
openalex publication_date 2013/08/13 · arxiv created 2013/09/14 · arxiv updated 2013/09/17 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We continue our study of operator algebras with contractive approximate identities (cais). In earlier papers we have introduced and studied a new notion of positivity in operator algebras, with an eye to extending certain C^*-algebraic results and theories to more general algebras. In the first part of this paper we do a more systematic development of this positivity and its associated ordering, proving many foundational facts. In much of this it is not necessary that the algebra have an approximate identity. In the second part we study interesting examples of operator algebras with cais, which in particular answer questions raised in previous papers in this series. Indeed the present work solves almost all of the open questions raised in these papers. Many of our results apply immediately to function algebras, but we will not take the time to point these out, although most of these applications seem new.