A Note on Sequential Product of Quantum Effects
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 al...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/520436 |
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| _version_ | 1832556733912842240 |
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| author | Chunyuan Deng |
| author_facet | Chunyuan Deng |
| author_sort | Chunyuan Deng |
| collection | DOAJ |
| description | 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. |
| format | Article |
| id | doaj-art-31bb01c9cc1d480abb7874168b0c5b79 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-31bb01c9cc1d480abb7874168b0c5b792025-02-03T05:44:26ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/520436520436A Note on Sequential Product of Quantum EffectsChunyuan Deng0School of Mathematics Science, South China Normal University, Guangzhou 510631, ChinaThe 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.http://dx.doi.org/10.1155/2013/520436 |
| spellingShingle | Chunyuan Deng A Note on Sequential Product of Quantum Effects Abstract and Applied Analysis |
| title | A Note on Sequential Product of Quantum Effects |
| title_full | A Note on Sequential Product of Quantum Effects |
| title_fullStr | A Note on Sequential Product of Quantum Effects |
| title_full_unstemmed | A Note on Sequential Product of Quantum Effects |
| title_short | A Note on Sequential Product of Quantum Effects |
| title_sort | note on sequential product of quantum effects |
| url | http://dx.doi.org/10.1155/2013/520436 |
| work_keys_str_mv | AT chunyuandeng anoteonsequentialproductofquantumeffects AT chunyuandeng noteonsequentialproductofquantumeffects |