A note on commutativity up to a factor of bounded operators

Authors:
Jian Yang and Hong-Ke Du

Translated by:

Journal:
Proc. Amer. Math. Soc. **132** (2004), 1713-1720

MSC (2000):
Primary 47A10

DOI:
https://doi.org/10.1090/S0002-9939-04-07224-7

Published electronically:
January 7, 2004

MathSciNet review:
2051132

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Abstract | References | Similar Articles | Additional Information

Abstract: In this note, we explore commutativity up to a factor for bounded operators and in a complex Hilbert space. Conditions on possible values of the factor are formulated and shown to depend on spectral properties of the operators. Commutativity up to a unitary factor is considered. In some cases, we obtain some properties of the solution space of the operator equation and explore the structures of and that satisfy for some A quantum effect is an operator on a complex Hilbert space that satisfies The sequential product of quantum effects and is defined by We also obtain properties of the sequential product.

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Additional Information

**Jian Yang**

Affiliation:
College of Mathematics and Information Science, Shaanxi Normal University, Xi’an 710062, P. R. China

Email:
yangjia0426@sina.com

**Hong-Ke Du**

Affiliation:
College of Mathematics and Information Science, Shaanxi Normal University, Xi’an 710062, P. R. China

Email:
hkdu@snnu.edu.cn

DOI:
https://doi.org/10.1090/S0002-9939-04-07224-7

Keywords:
Hilbert space,
commutator,
selfadjointness,
normal operator,
quantum effect

Received by editor(s):
October 25, 2002

Received by editor(s) in revised form:
January 9, 2003

Published electronically:
January 7, 2004

Additional Notes:
This work was partially supported by the National Natural Science Foundation of China

Communicated by:
Joseph A. Ball

Article copyright:
© Copyright 2004
American Mathematical Society