Tensor Algebras and Displacement Structure. Ii. Noncommutative Szeg¨o Polynomials
نویسندگان
چکیده
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 noncommuting variables. Thus, we obtain the recurrence equations and Christoffel-Darboux formulas for Szegö polynomials in several noncommuting variables, as well as a Favard type result. Also we continue to study a Szegö type kernel for the N-dimensional unit ball of an infinite dimensional Hilbert space.
منابع مشابه
Tensor Algebras and Displacement Structure . Iii . Asymptotic Properties
Astract. We continue to investigate some classes of Szegö type polynomials in several variables. We focus on asymptotic properties of these polynomials and we extend several classical results of G. Szegö to this setting.
متن کاملNormal Forms for Operators via Gröbner Bases in Tensor Algebras
We propose a general algorithmic approach to noncommutative operator algebras generated by linear operators using quotients of tensor algebras. In order to work with reduction systems in tensor algebras, Bergman’s setting provides a tensor analog of Gröbner bases. We discuss a modification of Bergman’s setting that allows for smaller reduction systems and tends to make computations more efficie...
متن کاملPositive Cone in $p$-Operator Projective Tensor Product of Fig`a-Talamanca-Herz Algebras
In this paper we define an order structure on the $p$-operator projective tensor product of Herz algebras and we show that the canonical isometric isomorphism between $A_p(Gtimes H)$ and $A_p(G)widehat{otimes}^p A_p(H)$ is an order isomorphism for amenable groups $G$ and $H$.
متن کاملAlgebras Associated to Pseudo-Roots of Noncommutative Polynomials are Koszul
Quadratic algebras associated to pseudo-roots of noncommutative polynomials have been introduced by I. Gelfand, Retakh, and Wilson in connection with studying the decompositions of noncommutative polynomials. Later they (with S. Gelfand and Serconek) shown that the Hilbert series of these algebras and their quadratic duals satisfy the necessary condition for Koszulity. It is proved in this note...
متن کاملOn the character space of vector-valued Lipschitz algebras
We show that the character space of the vector-valued Lipschitz algebra $Lip^{alpha}(X, E)$ of order $alpha$ is homeomorphic to the cartesian product $Xtimes M_E$ in the product topology, where $X$ is a compact metric space and $E$ is a unital commutative Banach algebra. We also characterize the form of each character on $Lip^{alpha}(X, E)$. By appealing to the injective tensor product, we the...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2002