ACTA issues

Criteria for the absence of eigenvalues of Jacobi matrices with matrix entries

Jan Janas

Acta Sci. Math. (Szeged) 80:1-2(2014), 261-273

Abstract. Selfadjoint Jacobi matrices with matrix entries and invertible blocks on the off-diagonals are considered. For three different classes of these matrices are given conditions which guarantee vanishing of their point spectra. Two of the conditions are extensions of the corresponding ones found by Damanik, Simon and Stolz for Jacobi matrices with scalar entries. The results are illustrated by two simple examples.

DOI: 10.14232/actasm-012-610-2

AMS Subject Classification (1991): 47B36, 47B39, 47B25

Keyword(s): Jacobi matrix/operator, spectral analysis, point spectrum, periodic sequences, commutator

Received December 11, 2012, and in revised form March 8, 2013. (Registered under 110/2012.)