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    • The non-equivalence of pseudo-Hermiticity and presence of antilinear symmetry

      Petr Siegl

      Volume 73 Issue 2 August 2009 pp 279-286

    • Fulltext

       

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      Permanent link:
      https://www.ias.ac.in/article/fulltext/pram/073/02/0279-0286

    • Keywords

       

      Pseudo-Hermiticity; antilinear symmetry; 𝐽-self-adjoint operators.

    • Abstract

       

      The non-equivalence of the presence of antilinear symmetry and pseudo-Hermiticity is shown for bounded operators. Two appropriate examples are operators with non-empty residual spectrum. The class of operators for which the equivalence holds is extended to the spectral operators of scalar type. The importance of 𝐽-self-adjointness is stressed and new proofs using this property are provided.

    • Author Affiliations

       

      Petr Siegl1 2 3

      1. Faculty of Nuclear Sciences and Physical Engineering, Prague, Czech Republic
      2. Department of Theoretical Physics, Nuclear Physics Institute, Academy of Sciences, Řeže, Czech Republic
      3. Laboratoire Astroparticule et Cosmologie, Universit ́e Paris 7, Paris, France

    • Dates

       
      Published
      August 2009

  • Pramana – Journal of Physics | News

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