Displaying similar documents to “Spectral deformations of Jacobi operators.”

Slowly oscillating perturbations of periodic Jacobi operators in l²(ℕ)

Marcin Moszyński (2009)

Studia Mathematica

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We prove that the absolutely continuous part of the periodic Jacobi operator does not change (modulo unitary equivalence) under additive perturbations by compact Jacobi operators with weights and diagonals defined in terms of the Stolz classes of slowly oscillating sequences. This result substantially generalizes many previous results, e.g., the one which can be obtained directly by the abstract trace class perturbation theorem of Kato-Rosenblum. It also generalizes several results concerning...

Unbounded Jacobi Matrices with Empty Absolutely Continuous Spectrum

Petru Cojuhari, Jan Janas (2008)

Bulletin of the Polish Academy of Sciences. Mathematics

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Sufficient conditions for the absence of absolutely continuous spectrum for unbounded Jacobi operators are given. A class of unbounded Jacobi operators with purely singular continuous spectrum is constructed as well.