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2013 A Note on Sequential Product of Quantum Effects
Chunyuan Deng
Abstr. Appl. Anal. 2013(none): 1-6 (2013). DOI: 10.1155/2013/520436

Abstract

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 I . For A , B ( ) , let A B = A 1 / 2 B A 1 / 2 be the sequential product and let A * B = ( A B + B A ) / 2 be the Jordan product of A , B ( ) . 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 A B and A * B imply that A and B have 3 × 3 diagonal operator matrix forms with I ( A ) ¯ ( B ) ¯ as an orthogonal projection on closed subspace ( A ) ¯ ( B ) ¯ being the common part of A and B . Moreover, some generalizations of results known in the literature and a number of new results for bounded operators are derived.

Citation

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Chunyuan Deng. "A Note on Sequential Product of Quantum Effects." Abstr. Appl. Anal. 2013 1 - 6, 2013. https://doi.org/10.1155/2013/520436

Information

Published: 2013
First available in Project Euclid: 27 February 2014

zbMATH: 1364.81152
MathSciNet: MR3096824
Digital Object Identifier: 10.1155/2013/520436

Rights: Copyright © 2013 Hindawi

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