On the product of the self-adjoint operators
A proof is given for the fact that the product of two self-adjoint operators, one of which is also positive, is again self-adjoint if and only if the product is normal. This theorem applies, in particular, if one operator is an orthogonal projection. In general, the positivity requirement cannot be...
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| Format: | Article |
| Language: | English |
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Wiley
1982-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Subjects: | |
| Online Access: | http://dx.doi.org/10.1155/S0161171282000751 |
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| _version_ | 1832563081048227840 |
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| author | Wulf Rehder |
| author_facet | Wulf Rehder |
| author_sort | Wulf Rehder |
| collection | DOAJ |
| description | A proof is given for the fact that the product of two self-adjoint operators, one of which is also positive, is again self-adjoint if and only if the product is normal. This theorem applies, in particular, if one operator is an orthogonal projection. In general, the positivity requirement cannot be dropped. |
| format | Article |
| id | doaj-art-5c78b7a542cd43d3bb06ea097ac48073 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 1982-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-5c78b7a542cd43d3bb06ea097ac480732025-02-03T01:20:58ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04251982-01-015481381610.1155/S0161171282000751On the product of the self-adjoint operatorsWulf Rehder0Department of Mathematics and Computer Science, University of Denver, Denver 80208, Colorado, USAA proof is given for the fact that the product of two self-adjoint operators, one of which is also positive, is again self-adjoint if and only if the product is normal. This theorem applies, in particular, if one operator is an orthogonal projection. In general, the positivity requirement cannot be dropped.http://dx.doi.org/10.1155/S0161171282000751self-adjoint operatorsnormal operatorscommutavity relations in quantum mechanics. |
| spellingShingle | Wulf Rehder On the product of the self-adjoint operators International Journal of Mathematics and Mathematical Sciences self-adjoint operators normal operators commutavity relations in quantum mechanics. |
| title | On the product of the self-adjoint operators |
| title_full | On the product of the self-adjoint operators |
| title_fullStr | On the product of the self-adjoint operators |
| title_full_unstemmed | On the product of the self-adjoint operators |
| title_short | On the product of the self-adjoint operators |
| title_sort | on the product of the self adjoint operators |
| topic | self-adjoint operators normal operators commutavity relations in quantum mechanics. |
| url | http://dx.doi.org/10.1155/S0161171282000751 |
| work_keys_str_mv | AT wulfrehder ontheproductoftheselfadjointoperators |