Some remarks on quasi-Hermitian operators

Camillo Trapani, Jean-Pierre Antoine

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14 Citations (Scopus)


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.
Original languageEnglish
Number of pages17
JournalJournal of Mathematical Physics
Publication statusPublished - 2014

All Science Journal Classification (ASJC) codes

  • Statistical and Nonlinear Physics
  • Mathematical Physics

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