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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.)
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