Free Calculus on Operator Algebras

Ilwoo Cho

ISBN 10: 3838325192 / ISBN 13: 9783838325194

Published by LAP LAMBERT Academic Publishing Sep 2010, 2010

About this Item

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.

Seller Inventory # 9783838325194

Bibliographic Details

• Title: Free Calculus on Operator Algebras
• Publisher: LAP LAMBERT Academic Publishing Sep 2010
• Publication Date: 2010
• Language: English
• ISBN 10: 3838325192
• ISBN 13: 9783838325194
• Binding: Taschenbuch
• Condition: Neu
• Dimensions: 220W x 150H x 6D millimeters 220 millimeters width by 150 millimeters height by 6 millimeters depth
• Weight: 155 grams

About this title

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.

About the Author

Master Degree (Math): Sungkyunkwan Univ., and Univ. of Iowa / PhD (Math): Univ. of Iowa / Current Position: Assistant Professor, St. Ambrose Univ., Dep. of Mathematics.