Operator (Quasi-)Similarity, Quasi-Hermitian Operators and All that

Camillo Trapani, Jean-Pierre Antoine

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Motivated by the recent developments of pseudo-Hermitian quantum mechanics,we analyze the structure generated by unbounded metric operators in a Hilbertspace. To that effect, we consider the notions of similarity and quasi-similarity betweenoperators and explore to what extent they preserve spectral properties. Thenwe study quasi-Hermitian operators, bounded or not, that is, operators that are quasisimilarto their adjoint and we discuss their application in pseudo-Hermitian quantummechanics. Finally, we extend the analysis to operators in a partial inner productspace (PIP-space), in particular the scale of Hilbert spaces generated by a single unboundedmetric operator.
Lingua originaleEnglish
Titolo della pubblicazione ospiteNon-Hermitian Hamiltonians in Quantum Physics
Numero di pagine21
Stato di pubblicazionePublished - 2016

Serie di pubblicazioni



All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)

Cita questo

Trapani, C., & Antoine, J-P. (2016). Operator (Quasi-)Similarity, Quasi-Hermitian Operators and All that. In Non-Hermitian Hamiltonians in Quantum Physics (pagg. 45-65). (SPRINGER PROCEEDINGS IN PHYSICS).