2002/03/07 by David P. Blecher, Blecher, David P., Roger R. Smith +3 · 1 citation
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #FOS: Mathematics #Functional Analysis (math.FA) #Holomorphic and Operator Theory #Operator Algebras (math.OA) #Primary 46L05 #Secondary 46L07 #math.FA #math.OA #msc:46L05 #msc:46L07
paper · pdf · doi:10.48550/arxiv.math/0203070
arxiv created 2002/03/07 · openalex publication_date 2002/03/07 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In [BEZ] the notion of a complete one-sided M-ideal for an operator space X was introduced as a generalization of Alfsen and Effros' notion of an M-ideal for a Banach space [AE72]. In particular, various equivalent formulations of complete one-sided M-projections were given. In this paper, some sharper equivalent formulations are given in the special situation that X = A, a C^*-algebra (in which case the complete left M-projections are simply left multiplication on A by a fixed orthogonal projection in A or its multiplier algebra). The proof of the first equivalence makes use of a technique which is of interest in its own right--a way of ``solving'' multi-linear equations in von Neumann algebras. This technique is also applied to show that preduals of von Neumann algebras have no nontrivial complete one-sided M-ideals. In addition, we show that in a C^*-algebra, the intersection of finitely many complete one-sided M-summands need not be a complete one-sided M-summand, unlike the classical situation.