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 metricoperators are in general assumed to be bounded, we analyze the structure generatedby unbounded metric operators in a Hilbert space. Following our previous work, weintroduce several generalizations of the notion of similarity between operators. Thenwe explore systematically the various types of quasi-Hermitian operators, bounded ornot. Finally, we discuss their application in the so-called pseudo-Hermitian quantummechanics.
|Number of pages||17|
|Journal||Journal of Mathematical Physics|
|Publication status||Published - 2014|
All Science Journal Classification (ASJC) codes
- Statistical and Nonlinear Physics
- Mathematical Physics