Related papers: Operators in the Fock-Toeplitz algebra
We develop an operator-theoretic approach to quaternionic Fock spaces, with emphasis on Carleson measures, Berezin transforms, and Toeplitz operators. We first introduce a global Gaussian $L^p$-framework on $\mathbb H$ for slice functions…
In this paper, we study the $L^{2}$-boundedness and $L^{2}$-compactness of a class of $h$-Fourier integral operators. These operators are bounded (respectively compact) if the weight of the amplitude is bounded (respectively tends to $0)$.
In this paper, we provide some sufficient conditions for the compactness of weighted composition operators on Dirichlet space. Furthermore, we characterize the numerical range of certain classes of weighted composition operators on…
Unbounded (and bounded) Toeplitz operators (TO) with rational symbols are analysed in detail showing that they are densely defined closed and have finite dimensional kernels and deficiency spaces. The latter spaces as well as the domains,…
We study positive Toeplitz operators on the Bergman spaces having the fast decreasing weight functions in a certain class. We give the characterizations for the boundedness and compactness of Toeplitz operators in terms of their Berezin…
In this paper we study the complex symmetry in the several variable Fock space by using the techniques of weighted composition operators and semigroups. We characterize unbounded weighted composition operators that are (real) complex…
In this paper we completely describe the numerical range of Toeplitz operators on weighted Bergman spaces with harmonic symbol. We also characterize the numerical range of weighted composition operators on weighted Bergman spaces and…
We study the weighted composition operators between the Lipschitz space and the space of bounded functions on the set of vertices of an infinite tree. We characterized the boundedness, the compactness, and the boundedness from below of…
Wiener-Hopf factorisation plays an important role in the theory of Toeplitz operators. We consider here Toeplitz operators in the Hardy spaces $H^p$ of the upper half-plane and we review how their Fredholm properties can be studied in terms…
We study operators on the Fock space on which by adjoining the rotation operators implements a continuous action of the circle group. We prove that this class of operators can be identified with the space of band-dominated operators on…
Volterra companion integral and multiplication operators with holomorphic symbols are studied for a large class of generalized Fock spaces on the complex plane $\CC$. The weights defining these spaces are radial and subject to a mild…
In this paper, we consider composition operators on weighted Hilbert spaces of analytic functions and observe that a formula for the essential norm, give a Hilbert-Schmidt characterization and characterize the membership in Schatten-class…
A new approach to problems of the Uncertainty Principle in Harmonic Analysis, based on the use of Toeplitz operators, has brought progress to some of the classical problems in the area. The goal of this paper is to develop and systematize…
We establish necessary and sufficient conditions for the boundedness and compactness of weighted composition operators acting on weighted Dirichlet spaces and determine the spectrum of a certain class of such operators. Our results extend…
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 make a progress towards describing the semi-commutants of Toeplitz operators on Fock-Sobolev spaces of nonnegative orders. We generalize the results in \cite{Bauer1,Qin}. For the certain symbol spaces, we obtain two Toeplitz operators…
For Toeplitz operators $T_f^{(t)}$ acting on the weighted Fock space $H_t^2$, we consider the semi-commutator $T_f^{(t)}T_g^{(t)}-T_{fg}^{(t)}$, where $t>0$ is a certain weight parameter that may be interpreted as Planck's constant $\hbar$…
We address the problem of studying the boundedness, compactness and weak compactness of the integral operators $T_g(f)(z)=\int_0^z f(\zeta)g'(\zeta)\,d\zeta$ acting from a Banach space $X$ into $H^\infty$. We obtain a collection of general…
A major open problem in the Theory of Toeplitz operators on the analytic Bergman space over the unit disk is the characterization of the commutant of a given Toeplitz operator--that is, the set of all bounded Toeplitz operators that commute…
The paper contains a survey of a class of Fourier integral operators defined by symbols with tempered weight. These operators are bounded (respectively compact) in $L^2$ if the weight of the amplitude is bounded (respectively tends to $0$).