One-Sided Projections on C*-algebras
| dc.creator | Blecher, David P. | |
| dc.creator | Smith, Roger R. | |
| dc.creator | Zarikian, Vrej | |
| dc.date | 2002-03-07 | |
| dc.date.accessioned | 2026-07-07T04:46:54Z | |
| dc.date.available | 2026-07-07T04:46:54Z | |
| dc.description | 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 $X = \mathcal{A}$, a $C^*$-algebra (in which case the complete left M-projections are simply left multiplication on $\mathcal{A}$ by a fixed orthogonal projection in $\mathcal{A}$ 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. | |
| dc.identifier | https://arxiv.org/abs/math/0203070 | |
| dc.identifier | http://arxiv.org/abs/math/0203070 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/63515 | |
| dc.subject | Operator Algebras | |
| dc.subject | Functional Analysis | |
| dc.subject | Primary 46L05; Secondary 46L07 | |
| dc.title | One-Sided Projections on C*-algebras | |
| dc.type | text |