Related papers: $C^*$-algebras generated by truncated Toeplitz ope…
Closed quantum surfaces of any genus are defined as subalgebras of the Toeplitz algebra by mimicking the classical construction of identifying arcs on the boundary of the (quantum) unit disk. Isomorphism classes obtained from different…
In this article we survey some of the recent goings-on in the classification programme of C$^*$-algebras, following the interesting link found between the Cuntz semigroup and the classical Elliott invariant and the fact that the Elliott…
In previous articles, a magnetic pseudodifferential calculus and a family of C*-algebras associated with twisted dynamical systems were introduced and the connections between them have been established. We extend this formalism to symbol…
We present and study C*-algebras generated by "periodic weighted creation operators" on the Fock space associated with an automorphism $\alpha$ on a C*-algebra $A$. These algebras can be viewed as generalized Bunce-Deddens algebras…
We use quantum harmonic analysis for densely defined operators to provide a simplified proof of the Berger-Coburn theorem for boundedness of Toeplitz operators. In addition, we revisit compactness and Schatten-class membership of densely…
Matrix valued truncated Toeplitz operators act on vector-valued model spaces. They represent a generalization of block Toeplitz matrices. A characterization of these operators analogue to the scalar case is obtained, as well as the…
We study algebraic properties of Toeplitz operators on Bergman spaces of polyanalytic functions on the unit disk. We obtain results on finite-rank commutators and semi-commutators of Toeplitz operators with harmonic symbols. We also raise…
We characterize matrix-valued asymmetric truncated Toeplitz operators (which are compressions of multiplication operators acting between two possibly different model spaces) by using compressed shifts, modified compressed shifts and shift…
We consider kernels of unbounded Toeplitz operators in $H^p(\mathbb C^+)$ in terms of a factorization of their symbols. We study the existence of a minimal Toeplitz kernel containing a given function in $H^p(\mathbb C^+)$, we describe the…
In this paper, we study matrix representations of truncated Toeplitz operators with respect to orthonormal bases which are invariant under a canonical conjugation map. In particular, we determine necessary and sufficient conditions for when…
In this paper we present some consequences of the description of matrix representations of asymmetric truncated Toeplitz operators acting between finite-dimensional model spaces. In particular, we prove that these operators can be…
We have introduced a notion of $C^*$-symbolic dynamical system in [K. Matsumoto: Actions of symbolic dynamical systems on $C^*$-algebras, to appear in J. Reine Angew. Math.], that is a finite family of endomorphisms of a $C^*$-algebra with…
We consider the class of positive bounded and semi-continuous functions defined on the two dimensional torus If f belongs to this class, then f will be considered as the symbol of a Toeplitz operator truncated on a triangle parametrised by…
This paper introduces the classically successful theory of Toeplitz operators on the Hardy space over the unit disk to a new domain in $\mathbb C^d$ -- the symmetrized polydisk.
The C*-algebra generated by the left-regular representation of $\mathbb{N}^n$ twisted by a $2$-cocycle is a Toeplitz extension of an $n$-dimensional noncommutative torus, on which each vector $r \in [0,\infty)^n$ determines a one-parameter…
We consider a class of C*-algebras associated to one parameter continuous tensor product systems of Hilbert modules, which can be viewed as continuous counterparts of Pimsner's Toeplitz algebras. By exhibiting a homotopy of…
We investigate Cuntz-Pimsner $C^*$-algebras associated with certain correspondences of the unit circle $\mathbb{T}$. We analyze these $C^*$-algebras by analogy with irrational rotation algebras $A_\theta$ and Cuntz algebras $\mathcal{O}_n$.…
Given a finitely aligned $k$-graph $\Lambda$, we let $\Lambda^i$ denote the $(k-1)$-graph formed by removing all edges of degree $e_i$ from $\Lambda$. We show that the Toeplitz-Cuntz-Krieger algebra of $\Lambda$, denoted by…
Motivated by the study of symmetries of C*-algebras, as well as by multivariate operator theory, we introduce the notion of an SU(2)-equivariant subproduct system of Hilbert spaces. We analyse the resulting Toeplitz and Cuntz-Pimsner…
Let $D$ be a bounded logarithmically convex complete Reinhardt domain in $\mathbb{C}^n$ centered at the origin. Generalizing a result for the one-dimensional case of the unit disk, we prove that the $C^*$-algebra generated by Toeplitz…