Abstract and Applied Analysis
Volume 2011 (2011), Article ID 702989, 13 pages
http://dx.doi.org/10.1155/2011/702989
Research Article

Completely Dissipative Maps and Stinespring's Dilation-Type Theorem on - -Algebras

Tian Zhou Xu

School of Mathematics, Beijing Institute of Technology, Beijing 100081, China

Received 18 July 2011; Accepted 6 September 2011

Academic Editor: Jean Michel Combes

Copyright © 2011 Tian Zhou Xu. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The notion of the completely dissipative maps on - -algebras is introduced. We show that a completely dissipative map induces a representation of a - -algebra. The classical Stinespring's dilation-type theorem is extended to a more general setting.