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Perturbation determinants and discrete spectra of semi-infinite non-self-adjoint Jacobi operators

77   0   0.0 ( 0 )
 Added by Leonid Golinskii
 Publication date 2021
  fields
and research's language is English




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We study the trace class perturbations of the half-line, discrete Laplacian and obtain a new bound for the perturbation determinant of the corresponding non-self-adjoint Jacobi operator. Based on this bound, we obtain the Lieb--Thirring inequalities for such operators. The spectral enclosure for the discrete spectrum and embedded eigenvalues are also discussed.



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79 - Leonid Golinskii 2021
We study the trace class perturbations of the whole-line, discrete Laplacian and obtain a new bound for the perturbation determinant of the corresponding non-self-adjoint Jacobi operator. Based on this bound, we refine the Lieb--Thirring inequality due to Hansmann--Katriel. The spectral enclosure for such operators is also discussed.
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