Free Calculus on Operator Algebras

Ilwoo Cho

ISBN 10: 3838325192 / ISBN 13: 9783838325194

Edité par LAP LAMBERT Academic Publishing Sep 2010, 2010

A propos de cet article

Neuware -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.Books on Demand GmbH, Überseering 33, 22297 Hamburg 92 pp. Englisch.

N° de réf. du vendeur 9783838325194

Détails bibliographiques

• Titre: Free Calculus on Operator Algebras
• Éditeur: LAP LAMBERT Academic Publishing Sep 2010
• Date de parution: 2010
• Langue: anglais
• ISBN à 10 chiffres: 3838325192
• ISBN à 13 chiffres: 9783838325194
• Reliure: Taschenbuch
• État de l'article: Neu
• Dimensions: 220 L x 150 H x 6 P (en millimètres) 220 millimètres de largeur par 150 millimètres de hauteur par 6 millimètres de profondeur
• Poids: 155 grammes

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Synopsis

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.