Geodesic
Classes of non-Hermitian operators with real eigenvalues
The electronic journal of linear algebra, Tome 21 (2010), pp. 98-109.

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: Classes of non-Hermitian operators that have only real eigenvalues are presented. Such operators appear in quantum mechanics and are expressed in terms of the generators of the Weyl-Heisenberg algebra. For each non-Hermitian operator A, a Hermitian involutive operator $\hat J$ such that A is $\hat J$ -Hermitian, that is, $\hat J A = A * \hat J$ , is found. Moreover, we construct a positive definite Hermitian Q such that A is Q-Hermitian, allowing for the standard probabilistic interpretation of quantum mechanics. Finally, it is shown that the considered matrices are similar to Hermitian matrices.
Classification : 47B50, 47A63
Keywords: infinite matrices, pseudo-Hermitian matrices, creation and annihilation operators, Kreĭn spaces 
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     author = {Bebiano, Natalia and Da Providencia, Joao and Da Providencia, Joao P.},
     title = {Classes of {non-Hermitian} operators with real eigenvalues},
     journal = {The electronic journal of linear algebra},
     pages = {98--109},
     publisher = {mathdoc},
     volume = {21},
     year = {2010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ELA_2010__21__a4/}
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Bebiano, Natalia; Da Providencia, Joao; Da Providencia, Joao P. Classes of non-Hermitian operators with real eigenvalues. The electronic journal of linear algebra, Tome 21 (2010), pp. 98-109. http://geodesic.mathdoc.fr/item/ELA_2010__21__a4/