ACTA issues

Weighted shift operators, orthogonal polynomials and chain sequences

Rupert Lasser, Josef Obermaier

Acta Sci. Math. (Szeged) 86:1-2(2020), 331-342

Abstract. The main purpose of this paper is to use chain sequences to study spectral properties of weighted shift operators $A$ and of tridiagonal operators $\Re A$. Characterizations of chain sequences and relations to Haar sequences are derived. We use these results to compare the spectral radius, the numerical radius and the norm of $A$ and $\Re A$. As an example we study orthogonal polynomials defined by a recursion formula with almost constant coefficients.

DOI: 10.14232/actasm-019-152-4

AMS Subject Classification (1991): 47B36, 47B37, 33C45

Keyword(s): weighted shift operators, Jacobi operators, chain sequences, orthogonal polynomials

received 21.11.2019, accepted 20.2.2020. (Registered under 152/2019.)