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

  • Jean-Pierre AntoineEmail author
  • Camillo Trapani
Conference paper
Part of the Springer Proceedings in Physics book series (SPPHY, volume 184)

Abstract

Motivated by the recent developments of pseudo-Hermitian quantum mechanics, we analyze the structure generated by unbounded metric operators in a Hilbert space. To that effect, we consider the notions of similarity and quasi-similarity between operators and explore to what extent they preserve spectral properties. Then we study quasi-Hermitian operators, bounded or not, that is, operators that are quasi-similar to their adjoint and we discuss their application in pseudo-Hermitian quantum mechanics. Finally, we extend the analysis to operators in a partial inner product space (pip-space), in particular the scale of Hilbert space s generated by a single unbounded metric operator.

Keywords

Hilbert Space Unitary Operator Symmetric Operator Real Spectrum Graph Norm 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Institut de Recherche en Mathématique et PhysiqueUniversité Catholique de LouvainLouvain-la-NeuveBelgium
  2. 2.Dipartimento di Matematica e InformaticaUniversità di PalermoPalermoItaly

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