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

Petr Siegl

doi:10.1007/s12043-009-0119-3

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

Petr Siegl^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	279-286
Number of pages	8
Journal	Pramana - Journal of Physics
Volume	73
Issue number	2
DOIs	https://doi.org/10.1007/s12043-009-0119-3
Publication status	Published - Aug 2009
Externally published	Yes

Keywords

Antilinear symmetry
J-self-adjoint operators
Pseudo-Hermiticity

ASJC Scopus subject areas

Physics and Astronomy(all)

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10.1007/s12043-009-0119-3

Cite this

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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.",

keywords = "Antilinear symmetry, J-self-adjoint operators, Pseudo-Hermiticity",

author = "Petr Siegl",

note = "Funding Information: The author is thankful to M Znojil and D Krejˇciˇr{\'i}k for valuable discussions. This work is supported by MSˇMT {\textquoteleft}Doppler Institute{\textquoteright} Project No. LC06002 and by the GACˇ R Grant No. 202/07/1307.",

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N2 - 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.

AB - 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.

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

Abstract

Keywords

ASJC Scopus subject areas

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