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

ISBN-13: 9783838325194 / Angielski / Miękka / 2009 / 92 str.

Ilwoo Cho

Opis

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.

O autorze

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