Related papers: Asymmetric truncated Toeplitz operators and conjug…
We characterize bounded and compact positive Toeplitz operators defined on the Bergman spaces over the Siegel upper half-space.
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 establish several relations between the determinants of the following structured matrices: Hankel matrices, symmetric Toeplitz + Hankel matrices and Toeplitz matrices. Using known results for the asymptotic behavior of…
We introduce an extended class of cross-Toeplitz operators which act between Fock--Segal--Bargmann spaces with different weights. It is natural to consider these operators in the framework of representation theory of the Heisenberg group.…
The resolvent convergence of self-adjoint operators via the technique of $\Gamma$-convergence of quadratic forms is adapted to incorporate complex Hilbert spaces. As an application, we find effective operators to the Dirichlet Laplacian…
We characterize the topologizability and power boundedness of convolution and dual convolution operators on power series spaces. We determine necessary conditions for a Toeplitz operator to be m-topologizable, and power bounded on…
We study Birkhoff-James orthogonality of bounded linear operators on complex Banach spaces and obtain a complete characterization of the same. By means of introducing new definitions, we illustrate that it is possible in the complex case,…
Some positive results about the composition of Toeplitz operators on the Segal-Bargmann space are presented. A Wick symbol where it is not possible to construct its associated Toeplitz operator is given.
This paper characterises the dual of the model space $K_I^1$, where $I$ is an inner function, intersected with the shifted Hardy space, $z H^1$. With this duality result, it is then shown that every bounded truncated Toeplitz operator on…
Using the unbounded picture of analytical K-homology, we associate a well-defined K-homology class to an unbounded symmetric operator satisfying certain mild technical conditions. We also establish an ``addition formula'' for the Dirac…
In this paper we study some geometric properties like parallelism, orthogonality and semi-rotundity in the space of bounded linear operators. We completely characterize parallelism of two compact linear operators between normed linear…
We prove a new criterion that guarantees self-adjointness of Toeplitz operator with unbounded operator-valued symbols. Our criterion applies, in particular, to symbols with Lipschitz continuous derivatives, which is the natural class of…
Using works of T.~Ando and L.~Gurvits, the well-known theorem of P.R.~Halmos concerning the existence of unitary dilations for contractive linear operators acting on Hilbert spaces recast as a result for $d$-tuples of contractive Hilbert…
We study the complex symmetric structure of weighted composition--differentiation operators of order $n $ on the weighted Bergman spaces $A_{\alpha}^2$ with respect to some conjugations. Then we provide some examples of these operators.
In this article, by considering $T=(T_1,\dots, T_d)$, an $d$-tuple of commuting contractions on a Hilbert space $\mathcal{H}$, we study $T$-Toeplitz operators which consists of bounded operators $X$ on $\mathcal{H}$ such that \[ T_i^*XT_i=X…
In this paper, we consider \emph{unbounded} weighted composition operators acting on Fock space, and investigate some important properties of these operators, such as $\calC$-selfadjoint (with respect to weighted composition conjugations),…
In this paper, we mainly study the hyponormality of dual Toeplitz operators on the orthogonal complement of the harmonic Bergman space. First we show that the dual Toeplitz operator with bounded symbol is hyponormal if and only if it is…
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 study the intertwining relations between analytic Toeplitz operators induced on the Hardy space H^2 by analytic functions bounded on the open unit disc. Our work centers on the connection between intertwining between the Toeplitz…
This paper mainly studies totally Abelian operators in the context of analytic Toeplitz operators on both the Hardy and Bergman space. When the symbol is a meromorphic function on $\mathbb{C}$, we establish the connection between totally…