Tuesday, July 23, 2013

1307.5644 (Jean-Pierre Antoine et al.)

Some remarks on quasi-Hermitian operators    [PDF]

Jean-Pierre Antoine, Camillo Trapani
A quasi-Hermitian operator is an operator that is similar to its adjoint in some sense, via a metric operator, i.e., a strictly positive self-adjoint operator. Whereas those metric operators are in general assumed to be bounded, we analyze the structure generated by unbounded metric operators in a Hilbert space. Following our previous work, we introduce several generalizations of the notion of similarity between operators. Then we explore systematically the various types of quasi-Hermitian operators, bounded or not. Finally we discuss their application in the so-called pseudo-Hermitian quantum mechanics.
View original: http://arxiv.org/abs/1307.5644

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