| Title | Monotone operator functions on C*-algebras |
| Authors | H Osaka, Sergei Silvestrov, J Tomiyama |
| Alternative Location | http://dx.doi.org/10.1142/S..., Restricted Access |
| Publication | INTERNATIONAL JOURNAL OF MATHEMATICS |
| Year | 2005 |
| Volume | 16 |
| Issue | 2 |
| Pages | 181 - 196 |
| Document type | Article |
| Status | Published |
| Quality controlled | Yes |
| Language | eng |
| Publisher | WORLD SCIENTIFIC PUBL CO |
| Abstract English | The article is devoted to investigation of classes of functions monotone as functions on general C-*-algebras that are not necessarily the C-*-algebra of all bounded linear operators on a Hilbert space as 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 with this class of monotone functions, providing at the same time a monotonicity characterization of subhomogeneous C-*-algebras. We use this result to generalize characterizations of commutativity of a C-*-algebra based on monotonicity conditions for a single function to characterizations of 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. |
| Keywords | operator monotone functions, subhomogeneous C*-algebra, |
| ISBN/ISSN/Other | ISSN: 0129-167X |
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