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Abstract and Applied Analysis
Volume 2013, Article ID 520436, 6 pages
Research Article

A Note on Sequential Product of Quantum Effects

School of Mathematics Science, South China Normal University, Guangzhou 510631, China

Received 29 May 2013; Revised 27 July 2013; Accepted 30 July 2013

Academic Editor: Ziemowit Popowicz

Copyright © 2013 Chunyuan Deng. 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.


The quantum effects for a physical system can be described by the set of positive operators on a complex Hilbert space that are bounded above by the identity operator . For , let be the sequential product and let be the Jordan product of . The main purpose of this note is to study some of the algebraic properties of effects. Many of our results show that algebraic conditions on and imply that and have diagonal operator matrix forms with as an orthogonal projection on closed subspace being the common part of and . Moreover, some generalizations of results known in the literature and a number of new results for bounded operators are derived.