In this monograph, we consider free calculus on operator algebras. In Part 1, we consider structure theorems for a C*-algebra generated by a finite family F of partial isometries on a Hilbert space. We show that, whenever such a family is given, there always exists the corresponding graph G of F. Moreover, the graph groupoid of G shows how this family F works on H. We realize that C*-algebra C*(F), generated by F is *-isomorphic to the groupoid C*-algebra generated by the graph groupoid of G, under suitable (embedding) representations. In Part 2, we determine free calculus on C*(F). Free calculus consists of the differentiation, and the integration, like the usual calculus. The fundamental properties of them are studied. Also, we investigate free calculus on arbitrary C*-algebras. In Part 3, we extend the free calculus in the sense of Part 2 to that on groupoid C*-dynamical systems.
| Autorius: | Ilwoo Cho |
| Leidėjas: | LAP LAMBERT Academic Publishing |
| Išleidimo metai: | 2010 |
| Knygos puslapių skaičius: | 92 |
| ISBN-10: | 3838325192 |
| ISBN-13: | 9783838325194 |
| Formatas: | 220 x 150 x 6 mm. Knyga minkštu viršeliu |
| Kalba: | Anglų |
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