Related papers: Toeplitz Quantization of a Free $ * $-Algebra
The theory of Toeplitz quantization presented in our previous paper is extended and further developed to include diverse and interesting non-commutative realizations of the classical Euclidean plane. This is done using Hilbert spaces of…
We define co-Toeplitz operators, a new class of Hilbert space operators, in order to define a co-Toeplitz quantization scheme that is dual to the Toeplitz quantization scheme introduced by the author in the setting of symbols that come from…
The author has introduced in a recent paper a new class of operators, called co-Toeplitz operators, with symbols in a co-algebra. This is the categorical dual to Toeplitz operators which have symbols in an algebra. The mapping from a symbol…
This note is a follow-up to a recent paper by the author. Most of that theory is now realized in a new setting where the vector space of symbols is not necessarily an algebra nor is it equipped with an inner product, although it does have a…
Toeplitz quantization is defined in a general setting in which the symbols are the elements of a possibly non-commutative algebra with a conjugation and a possibly degenerate inner product. We show that the quantum group $SU_q(2)$ is such…
We study Toeplitz operators on Hilbert spaces of holomorphic functions on symmetric domains, and more generally on certain algebraic subvarieties, determined by integration over boundary orbits of the underlying domain. The main result…
Motivated by the interplay between quadratic algebras, noncommutative geometry, and operator theory, we introduce the notion of quadratic subproduct systems of Hilbert spaces. Specifically, we study the subproduct systems induced by a…
We obtain an analogue of Coburn's description of the Toeplitz algebra in the setting of truncated Toeplitz operators. As a byproduct, we provide several examples of complex symmetric operators which are not unitarily equivalent to truncated…
We give a simplified proof of the Berger-Coburn theorem on the boundedness of Toeplitz operators and extend this theorem to the setting of $p$-Fock spaces $(1\leq p \leq \infty)$. We present an overview of recent results by various authors…
We describe the C*-algebra generated by an irreducible Toeplitz operator $T_{\psi}$, with continuous symbol $\psi $ on the unit circle $\mathbb{T}$, and finitely many composition operators on the Hardy space $H^2$ induced by certain…
The Fock space consists of all entire functions which are square integrable with respect to Gauss measure. The Toeplitz algebra is the C*-algebra generated by the Toeplitz operator with bounded symbol on the Fock space. In this paper, we…
In this paper we study the Toeplitz algebra, which is generated by Toeplitz operators with bounded symbols on the Fock space $F^p_{\alpha}$. We show that the Toeplitz algebra coincides with each of the algebras generated by band-dominated,…
We find necessary and sufficient conditions for the product of two truncated Toeplitz operators on a model space to itself be a truncated Toeplitz operator, and as a result find a characterization for the maximal algebras of bounded…
For any given bounded symmetric domain, we prove the existence of commutative $C^*$-algebras generated by Toeplitz operators acting on any weighted Bergman space. The symbols of the Toeplitz operators that generate such algebras are defined…
We define and analyze Toeplitz operators whose symbols are the elements of the complex quantum plane, a non-commutative, infinite dimensional algebra. In particular, the symbols do not come from an algebra of functions. The process of…
In this paper, we consider the relation between Toeplitz operators and elements in von Neumann algebras generated by certain graph groupoids.
We consider commutative C* -algebras of Toeplitz operators in the weighted Bergman space on the unit ball in $\mathbb{C}^{\mathbf{n}}$. For the algebras of elliptic type we find a new representation, namely as the algebra of operators which…
We study $C^*$-algebras generated by Toeplitz operators acting on the standard weighted Bergman space $\mathcal{A}_{\lambda}^2(\mathbb{B}^n)$ over the unit ball $\mathbb{B}^n$ in $\mathbb{C}^n$. The symbols $f_{ac}$ of generating operators…
We generalize some earlier results on a Berezin-Toeplitz type of quantization on Hilbert spaces built over certain matrix domains. In the present, wider setting, the theory could be applied to systems possessing several kinematic and…
For three standard models of commutative algebras generated by Toeplitz operators in the weighted analytic Bergman space on the unit disk, we find their representations as the algebras of bounded functions of certain unbounded self-adjoint…