Convolution structures associated with orthogonal polynomials

Abstract We study Banach algebras associated with orthogonal polynomials via the product formula. Sufficient conditions under which the spectrum of this algebra coincides with the support of the orthogonalizing measure are given. The results apply to the Jacobi polynomials P(n(α,β) with α ⩾ β and α + β + 1 ⩾ 0.