Related papers: The eigenvalues of limits of radial Toeplitz opera…
We present some new upper and lower bounds for the numerical radius of bounded linear operators on a complex Hilbert space and show that these are stronger than the existing ones. In particular, we prove that if $A$ is a bounded linear…
We study Toeplitz operators on the Bargmann space, with Toeplitz symbols given by exponentials of complex quadratic forms. We show that the boundedness of the corresponding Weyl symbols is necessary for the boundedness of the operators,…
We study compact operators on the Bergman space of the Thullen domain defined by $\{(z_1,z_2)\in \mathbb C^2: |z_1|^{2p}+|z_2|^2<1\}$ with $p>0$ and $p\neq 1$. The domain need not be smooth nor have a transitive automorphism group. We give…
We consider eigenvalue sums of Schr\"odinger operators $-\Delta+V$ on $L^2(\R^d)$ with complex radial potentials $V\in L^q(\R^d)$, $q<d$. We prove quantitative bounds on the distribution of the eigenvlaues in terms of the $L^q$ norm of $V$.…
In this paper we consider magnetic Schroedinger operators on the two-dimensional unit disk with a radially symmetric magnetic field which explodes to infinity at the boundary. We prove a bound for the eigenvalue moments and a bound for the…
We obtain a Szeg\"o limit theorem for a family of Toeplitz operators defined on the weighted Bergman space of the unit ball $\mathbb{B}_{n}$. The symbols of these operators are supported on some isotropic or co-isotropic submanifold $\Gamma…
For $\alpha>-1$, let $A^2_{\alpha}$ be the corresponding weighted Bergman space of the unit ball in $\mathbb{C}^n$. For a bounded measurable function $f$, let $T_f$ be the Toeplitz operator with symbol $f$ on $A^2_{\alpha}$. This paper…
We present new upper and lower bounds for the numerical radius of a bounded linear operator defined on a complex Hilbert space, which improve on the existing bounds. Among many other inequalities proved in this article, we show that for a…
As a class of compact operators on the $\ell^2-$valued Bergman space $A^2_\alpha (\mathbb B_n, \ell^2)$ on the unit ball $\mathbb B_n,$ we study Toeplitz operators with $BMO^1_\alpha (\mathbb B_n, \mathcal L(\ell^2))$ operator-valued…
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…
The paper discusses the spectrum of Toeplitz operators in Bargmann spaces. Our Toeplitz operators have real symbols with a variable sign and a compact support. A class of examples is considered where the asymptotics of the eigenvalues of…
In the present paper, we study the boundedness and compactness of Toeplitz operators and Berezin-type operators between different weighted Bergman spaces over tubular domains in $\mathbb{C}^n$. We establish their connection with Carleson…
We develope new lower bounds for the $A$-numerical radius of semi-Hilbertian space operators, and applying these bounds we obtain upper bounds for the $A$-numerical radius of the commutators of operators. The bounds obtained here improve on…
We consider Toeplitz operators with bounded symbol acting on the Bergman space of the unit disk and assess their hyponormality. We will mainly be concerned with the symbol $\varphi(z)=z^{n}|z|^{2s}+a(t)\bar{z}^{m}|z|^{2t}$, where $s$ and…
We obtain Szeg\H{o}-type Limit Theorems in the setting of Reproducing Kernel Hilbert Spaces on discs in $\mathbb{C}$. From this, we derive a formula for the density of the eigenvalues of compressions of Toeplitz operators. Examples for the…
Let $A$ be a positive bounded operator on a Hilbert space $\big(\mathcal{H}, \langle \cdot, \cdot\rangle \big)$. The semi-inner product ${\langle x, y\rangle}_A := \langle Ax, y\rangle$, $x, y\in\mathcal{H},$ induces a seminorm…
We provide asymptotic formulas for the Bergman projector and Berezin-Toeplitz operators on a compact K{\"a}hler manifold. These objects depend on an integer N and we study, in the limit N $\rightarrow$ +$\infty$, situations in which one can…
Denote by w(A) the numerical radius of a bounded linear operator A acting on Hilbert space. Suppose that A is invertible and that the numerical radius of A and of its inverse are no greater than 1+e for some non-negative e. It is shown that…
We consider a class of compact Toeplitz operators on the Bergman space on the unit disk. The symbols of operators in our class are assumed to have a sufficiently regular power-like behaviour near the boundary of the disk. We compute the…
Let $A=\begin{bmatrix} A_{ij} \end{bmatrix}$ be an $n\times n$ operator matrix, where each $A_{ij}$ is a bounded linear operator on a complex Hilbert space. Among other numerical radius bounds, we show that $w(A)\leq w(\hat{A})$, where…