Open projections in operator algebras. II: Compact projections
type: Item
instance of: scholarly article
zbMATH Open document ID: 1259.46046
author: David P. Blecher
author: Matthew Neal
published in: Studia Mathematica
publication date: 2012-06-13T00:00:00Z
full work available at URL: https://arxiv.org/abs/1109.5347
Mathematics Subject Classification ID: 46L05
Mathematics Subject Classification ID: 47L30
Mathematics Subject Classification ID: 46L07
Mathematics Subject Classification ID: 46L30
Mathematics Subject Classification ID: 47L75
zbMATH DE Number: 6046227
zbMATH Keywords: non-self-adjoint operator algebras
zbMATH Keywords: open projection
zbMATH Keywords: closed projection
zbMATH Keywords: compact projection
zbMATH Keywords: faces
zbMATH Keywords: semi-exposed faces
zbMATH Keywords: ideals
zbMATH Keywords: noncommutative Urysohn lemma
zbMATH Keywords: hereditary subalgebra
MaRDI profile type: Publication
OpenAlex ID: W2964205715
arXiv ID: 1109.5347
DOI: 10.4064/SM209-3-1
title: Open projections in operator algebras. II: Compact projections
review text: This paper continues the authors' investigations into the generalization of the properties of \(C^*\)-algebras to the larger class of approximately unital (not necessarily self-adjoint) operator algebras. The crucial property of such an algebra \(A\) is that the intersection of the closed unit ball in \(A\) with the set of elements in the closed unit ball centered at the unit in \(A\) (adjoined if necessary) shares many of the properties of the positive part of the unit ball in a \(C^*\)-algebra.NEWLINENEWLINE In the first part of this paper [ibid. 208, No. 2, 117--150 (2012; Zbl 1259.46045)], the authors studied various generalizations of the `openness' of projections in the biduals of \(C^*\)-algebras and their consequences. In this second part, they concern themselves with the generalization of `compactness', of projections in the second duals of \(C^*\)-algebras. The fact that many of their results are predictable should not detract from the interesting nature of their generalization to a wide class of non-self-adjoint operator algebras.
reviewed by: C. M. Edwards
description: scientific article; zbMATH DE number 6046227