Monotone operator functions on $C^*$-algebra
| dc.creator | Osaka, Hiroyuki | |
| dc.creator | Silvestrov, Sergei D. | |
| dc.creator | Tomiyama, Jun | |
| dc.date | 2003-11-06 | |
| dc.date.accessioned | 2026-07-07T05:02:39Z | |
| dc.date.available | 2026-07-07T05:02:39Z | |
| dc.description | The article is devoted to investigation of classes of functions monotone as functions on general $C^*$-algebras that are not necessarily the $C^*$-algebras of all bounded linear operators on a Hilbert space as it is in classical case of matrix and operator monotone functions. We show that for general $C^*$-algebras the classes of monotone functions coincide with the standard classes of matrix and operator monotone functions. For every class we give exact characterization of $C^*$-algebras that have this class of monotone functions, providing at the same time a monotonicity characterization of subhomogeneous $C^*$-algebras. We use this characterization to generalize one function based monotonicity conditions for commutativity of a $C^*$-algebra, to one function based monotonicity conditions for subhomogeneity. As a $C^*$-algebraic counterpart of standard matrix and operator monotone scaling, we investigate, by means of projective $C^*$-algebras and relation lifting, the existence of $C^*$-subalgebras of a given monotonicity class. | |
| dc.description | 16 pages, LaTex | |
| dc.identifier | https://arxiv.org/abs/math/0311072 | |
| dc.identifier | http://arxiv.org/abs/math/0311072 | |
| dc.identifier.uri | http://salesiana.dossiersoluciones.com/handle/123456789/69089 | |
| dc.subject | Operator Algebras | |
| dc.subject | 47L65; 37B05, 37B20, 47L55 | |
| dc.title | Monotone operator functions on $C^*$-algebra | |
| dc.type | text |