|
|||||
|
|
A note on commutativity up to a factor of bounded operators |
|
| Authors: | Jian Yang Hong-Ke Du |
| Affiliation: | College of Mathematics and Information Science, Shaanxi Normal University, Xi'an 710062, P. R. China ; College of Mathematics and Information Science, Shaanxi Normal University, Xi'an 710062, P. R. China |
| 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. |
| Keywords: | Hilbert space commutator selfadjointness normal operator quantum effect |
| 点击此处可从《Proceedings of the American Mathematical Society》浏览原始摘要信息 | |
| 点击此处可从《Proceedings of the American Mathematical Society》下载全文 | |