In this paper we continue to explore the connection between tensor algebras and displacement structure. We focus on recursive orthonormalization and we develop an analogue of the Szegö-type theory of orthogonal polynomials in the unit circle for several non-commuting variables. Thus we obtain recurrence equations and Christoffel-Darboux formulas for Szegö polynomials in several non-commuting variables, as well as a Favard type result. Also, we continue to study a Szegö-type kernel for the -dimensional unit ball of an infinite-dimensional Hilbert space.
Cite this article
Tiberiu Constantinescu, J. L. Johnson, Tensor Algebras and Displacement Structure II: Non-Commutative Szegö Polynomials. Z. Anal. Anwend. 21 (2002), no. 3, pp. 611–626DOI 10.4171/ZAA/1098