相关论文: Factoring in Non-commutative Analytic Toeplitz Alg…

A free semigroupoid algebra is the weak operator topology closed algebra generated by the left regular representation of a directed graph. We establish lattice isomorphisms between ideals and invariant subspaces, and this leads to a…

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…

The parabolic algebra A_p is the weakly closed algebra on L^2(R) generated by the unitary semigroup of right translations and the unitary semigroup of multiplication by the analytic exponential functions e^{i\lambda x}, \lambda \geq 0. This…

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…

Let $G$ be a locally compact abelian Hausdorff topological group which is non-compact and whose Pontryagin dual $\Gamma$ is partially ordered. Let $\Gamma^{+}\subset\Gamma$ be the semigroup of positive elements in $\Gamma$. The Hardy space…

We give a definition of Toeplitz matrix acting on the $\ell^2$-space of an imprimitivity bimodule $X$ over a $C^*$-algebra $A$. We characterize the set of Toeplitz matrices as the closure in a certain topology of the image of the left…

We study the structure of weakly-closed nonself-adjoint algebras arising from representations of single vertex 2-graphs. These are the algebras generated by 2 isometric tuples which satisfy a certain commutation relation. We show that these…

We generalize several results on Toeplitz operators over reflexive, standard weighted Fock spaces $F_t^p$ to the non-reflexive cases $p = 1, \infty$. Among these results are the characterization of compactness and the Fredholm property of…

We compute an explicit representation of the (topological) automorphism group or a particular Toeplitz subshift. The automorphism group is a (non-finitely generated) subgroup of rational numbers under addition and the shift map corresponds…

We consider an action of the circle group, T on a von Neumann algebra, M. Similarly to the case when the algebra of essentially bounded functions on T is acted upon by translations, we define the generalized Hardy subspace of H,where H is…

Let $\mathfrak{T}$ denote the full Toeplitz algebra on the Bergman space of the unit ball $\mathbb{B}_n.$ For each subset $G$ of $L^{\infty},$ let $\mathfrak{CI}(G)$ denote the closed two-sided ideal of $\mathfrak{T}$ generated by all…

In this paper, we study Toeplitz algebras generated by certain class of Toeplitz operators on the $p$-Fock space and the $p$-Bergman space with $1<p<\infty$. Let BUC($\mathbb C^n$) and BUC($\mathbb B_n$) denote the collections of bounded…

A functor from the category of directed trees with inclusions to the category of commutative C*-algebras with injective *-homomorphisms is constructed. This is used to define a functor from the category of directed graphs with inclusions to…

We show an isomorphism between an algebra which is naturally constructed from the Toeplitz algebra generated by d-shifts, and an ideal of the C * -algebra of the (2d + 1)-dimensional Heisenberg group. This is a particular case of a more…

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…

We prove that Toeplitz operators are norm dense in the Toeplitz algebra $\mathfrak{T}(L^\infty)$ over the weighted Bergman space $\mathcal{A}^2_\nu(\Omega)$ of a bounded symmetric domain $\Omega\subset\mathbb{C}^n$. Our methods use…

A very first step to develop non-commutative algebraic geometry is the arithmetic of polynomials in non-commuting variables over a commutative field, that is, the study of elements in free associative algebras. This investigation is…

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 Hopf algebra of word-quasi-symmetric functions ($\WQSym$), a noncommutative generalization of the Hopf algebra of quasi-symmetric functions, can be endowed with an internal product that has several compatibility properties with the…

We review the theory of Toeplitz extensions and their role in operator K-theory, including Kasparov's bivariant K-theory. We then discuss the recent applications of Toeplitz algebras in the study of solid state systems, focusing in…