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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1982-01-01
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Series: | International Journal of Mathematics and Mathematical Sciences |
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Online Access: | http://dx.doi.org/10.1155/S0161171282000751 |
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doaj-5c78b7a542cd43d3bb06ea097ac480732020-11-25T00:53:13ZengHindawi LimitedInternational 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. |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Wulf Rehder |
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. |
author_facet |
Wulf Rehder |
author_sort |
Wulf Rehder |
title |
On the product of the self-adjoint operators |
title_short |
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_sort |
on the product of the self-adjoint operators |
publisher |
Hindawi Limited |
series |
International Journal of Mathematics and Mathematical Sciences |
issn |
0161-1712 1687-0425 |
publishDate |
1982-01-01 |
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. |
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 |
_version_ |
1725238666998054912 |