We study nonsymmetric second order diierence operators acting in the Hilbert spacè 2 and describe the resolvent set and the essential spectrum of such operators in terms of related formal orthogonal polynomials. As an application, we obtain new results on the growth of orthonormal polynomials outside and inside the support of the underlying measure of orthogonality.

Abstract We focus on the problem of generalized orthogonality matrix operators in operator spaces. Especially, ℬ ( l 1 n , p ) ≤ <m:m...