On the spectrum of tridiagonal operators in the context of orthogonal polynomials

Abstract The basis for our studies is a large class of orthogonal polynomial sequences (Pₙ) ₍ { {₍}₀} (P n) n ∈ N 0, which is normalized by Pₙ (x₀) =1 P n (x 0) = 1 for all n {N}₀ n ∈ N 0 where the coefficients in the three-term recurrence relation are bounded. The goal is to check if x₀ {R} x 0 ∈ R is in the support of the orthogonalization measure μ. For this purpose, we use, among other things, a result of G. H. Hardy concerning Cesàro operators on weighted l² l 2 -spaces. These investigations generalize ideas from Lasser et al. (Arch Math 100: 289–299, 2013).