Opuscula Math. 36, no. 6 (2016), 807-818
http://dx.doi.org/10.7494/OpMath.2016.36.6.807

Opuscula Mathematica

On the spectrum of periodic perturbations of certain unbounded Jacobi operators

Abstract. It is known that a purely off-diagonal Jacobi operator with coefficients $$a_n=n^{\alpha}$$, $$\alpha\in(0,1]$$, has a purely absolutely continuous spectrum filling the whole real axis. We show that a 2-periodic perturbation of these operators creates a non trivial gap in the spectrum.

Keywords: essential spectrum, spectral gap, periodic perturbation.

Mathematics Subject Classification: 47A10, 47B36, 39A70.

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