Characterizations of essential ideals as operator modules over C*-algebras
| dc.creator | Kaneda, Masayoshi | |
| dc.creator | Paulsen, Vern Ival | |
| dc.date | 2001-02-16 | |
| dc.date.accessioned | 2026-07-07T04:40:13Z | |
| dc.date.available | 2026-07-07T04:40:13Z | |
| dc.description | In this paper we give characterizations of essential left ideals of a C*-algebra $A$ in terms of their properties as operator $A$-modules. Conversely, we seek C*-algebraic characterizations of those ideals $J$ in $A$ such that $A$ is an essential extension of $J$ in various categories of operator modules. In the case of two-sided ideals, we prove that all the above concepts coincide. We obtain results, analogous to {M. Hamana's} results, which characterize the injective envelope of a C*-algebra as a maximal essential extension of the C*-algebra, but with completely positive maps replaced by completely bounded module maps. By restricting to one-sided ideals, module actions reveal clear differences which do not show up in the two-sided case. Throughout this paper, module actions are crucial. | |
| dc.identifier | https://arxiv.org/abs/math/0102134 | |
| dc.identifier | http://arxiv.org/abs/math/0102134 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/60959 | |
| dc.subject | Operator Algebras | |
| dc.subject | 46H10, 46H25, 46L07 (Primary) 46A22, 46L05, 46L08, 46M10, 47D15, 47L25 (Secondary) | |
| dc.title | Characterizations of essential ideals as operator modules over C*-algebras | |
| dc.type | text |