Related papers: Toeplitz Operators in a Symmetrically-Normed Ideal
We characterise the boundedness of a Toeplitz operator on the Bergman space with an L^1 symbol.We also prove that the compactness of a Toeplitz operator on the Bergman space with an L^1 symbol is completely determined by the boundary…
We study the restriction operator from the Bergman space of a domain in $\mathbb{C}^n$ to the Bergman space of a non-empty open subset of the domain. We relate the restriction operator to the Toeplitz operator on the Bergman space of the…
In this paper, we study Toeplitz operators on the weighted harmonic Bergman spaces with nonnegative symbols, the weights we choose here are Muckenhoupt A_2 weights. Results obtained include characterizations of bounded Toeplitz operators,…
In this paper we study mapping properties of Toeplitz-like operators on weighted Bergman spaces of bounded strongly pseudconvex domains in $\mathbb{C}^n$. In particular we prove that a Toeplitz operator built using as kernel a weighted…
Asymmetric dual truncated Toeplitz operators acting between the orthogonal complements of two (eventually different) model spaces are introduced and studied. They are shown to be equivalent after extension to paired operators on…
We investigate the lifting property of modulation spaces and construct explicit isomorpisms between them. For each weight function $\omega$ and suitable window function $\fy $, the Toeplitz operator (or localization operator) $\tp_\fy…
In this paper we characterize the Schatten $p$ class membership of Toeplitz operators with positive measure symbols acting on generalized Fock spaces for the full range $0 < p < \infty$.
The Fredholm property of Toeplitz operators on the $p$-Fock spaces $F_\alpha^p$ on $\mathbb{C}^n$ is studied. A general Fredholm criterion for arbitrary operators from the Toeplitz algebra $\mathcal{T}_{p,\alpha}$ on $F_\alpha^p$ in terms…
Truncated Toeplitz operators are compressions of Toeplitz operators on model spaces; they have received much attention in the last years. This survey article presents several recent results, which relate boundedness, compactness, and…
This is a review paper based on the series of our papers devoted to a structure of true-poly-analytic Bergman function spaces over the upper half-plane in the complex plane and to a detailed study of properties of Toeplitz operators with…
The paper considers bounded linear radial operators on the polyanalytic Fock spaces $\mathcal{F}_n$ and on the true-polyanalytic Fock spaces $\mathcal{F}_{(n)}$. The orthonormal basis of normalized complex Hermite polynomials plays a…
A certain class of matrix-valued Borel matrix functions is introduced and it is shown that all functions of that class naturally operate on any operator T in a finite type I von Neumann algebra M in a way such that uniformly bounded…
In this paper, it is shown that some new phenomenon related to the spectra of Toeplitz operators with bounded harmonic symbols on the Bergman space. On the one hand, we prove that the spectrum of the Toeplitz operator with symbol…
One of the major questions in the theory of Toeplitz operators on the Bergman space over the unit disk $\mathbb D$ in the complex plane $\mathbb C$ is a complete description of the commutant of a given Toeplitz operator, that is the set of…
Unlike Toeplitz operators on $H^2$, truncated Toeplitz operators do not have a natural matricial characterization. Consequently, these operators are difficult to study numerically. In this note we provide criteria for a matrix with distinct…
We investigate truncated Toeplitz operators belonging to the Schatten ideals. We completely characterize such operators when they have an analytic symbol or belong to the ideal of Hilbert-Schmidt operators. We also study model spaces…
This paper contains a further analysis of the Toeplitz-like operators $T_\omega$ on $H^p$ with rational symbol $\omega$ having poles on the unit circle that were previously studied in [5.6]. Here the adjoint operator $T_\omega^*$ is…
In this paper, for $p> 1 $ and $r \ge 1$ we provide a complete characterization of the positive Borel measures $\mu$ on the unit ball $\B_n$ of $\mathbb {C}^n$ for which the induced Toeplitz operator $T_\mu$ is $r$-summing on the Bergman…
We characterize operator-theoretic properties (boundedness, compactness, and Schatten class membership) of Toeplitz operators with positive measure symbols on Bergman spaces of holomorphic hermitian line bundles over K\"ahler…
We study subnormal Toeplitz operators on the vector-valued Hardy space of the unit circle, along with an appropriate reformulation of P.R. Halmos's Problem 5: Which subnormal block Toeplitz operators are either normal or analytic? We extend…