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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Bibliographic Details
Main Author:	Wulf Rehder
Format:	Article
Language:	English
Published:	Hindawi Limited 1982-01-01
Series:	International Journal of Mathematics and Mathematical Sciences
Subjects:	self-adjoint operators normal operators commutavity relations in quantum mechanics.
Online Access:	http://dx.doi.org/10.1155/S0161171282000751

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spelling	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

On the product of the self-adjoint operators

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