Free Calculus on Operator Algebras: Operator Algebraic Calculus Induced by Certain Operators

ILWOO CHO

ISBN 10: 3838325192 / ISBN 13: 9783838325194

Published by LAP Lambert Academic Publishing, 2009

About this Item

92 pages. 8.66x5.91x0.21 inches. In Stock.

Seller Inventory # 3838325192

Bibliographic Details

• Title: Free Calculus on Operator Algebras: Operator Algebraic Calculus Induced by Certain Operators
• Publisher: LAP Lambert Academic Publishing
• Publication Date: 2009
• Language: English
• ISBN 10: 3838325192
• ISBN 13: 9783838325194
• Binding: Paperback
• Condition: Brand New
• Weight: 0.19 kilograms

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.