Complex-self-adjointness

@article{Cmara2022Complexselfadjointness,
  title={Complex-self-adjointness},
  author={M. Cristina C{\^a}mara and David Krej{\vc}iř{\'i}k},
  journal={Analysis and Mathematical Physics},
  year={2022},
  volume={13}
}
We develop the concept of operators in Hilbert spaces which are similar to their adjoints via antiunitary operators, the latter being not necessarily involutive. We discuss extension theory, refined polar and singular-value decompositions, and antilinear eigenfunction expansions. The study is motivated by physical symmetries in quantum mechanics with non-self-adjoint operators. 
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References

SHOWING 1-10 OF 20 REFERENCES

The Pauli equation with complex boundary conditions

We consider one-dimensional Pauli Hamiltonians in a bounded interval with possibly non-self-adjoint Robin-type boundary conditions. We study the influence of the spin–magnetic interaction on the…

Conjugations and complex symmetric block Toeplitz operators on the weighted Hardy space

  • E. KoJ. LeeJongrak Lee
  • Materials Science
    Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas
  • 2021
In this paper, we study block conjugations on the weighted Hardy space Hρ(Cn)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb}…

Conjugations in $$L^2$$ and their invariants

<jats:p>Conjugations in space <jats:inline-formula><jats:alternatives><jats:tex-math>$$L^2$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msup>…

Complex symmetric completions of partial operator matrices

ABSTRACT We study complex symmetric completions of a partial operator matrix which specified part is an operator from a Hilbert space into a closed proper subspace. We give necessary and sufficient…

Direct methods of qualitative spectral analysis of singular differential operators

Elements of spectral theory without the spectral theorem

On complex symmetric Toeplitz operators

Perturbation theory for linear operators

Spectral Theory and Differential Operators

This book gives an account of those parts of the analysis of closed linear operators acting in Banach or Hilbert spaces that are relevant to spectral problems involving differential operators, and…

The Physics of Time Reversal

A filler for a continuous cigarette filter rod is formed by feeding a wide band of filaments of filter material on to a slower moving surface, to which suction is applied so that the band is axially…