Related papers: Trace class criteria for Toeplitz and composition …

We find a concrete integral formula for the class of generalized Toeplitz operators $T_a$ in Bergman spaces $A^p$, $1<p<\infty$, studied in an earlier work by the authors. The result is extended to little Hankel operators. We give an…

We generalize several results on Toeplitz operators over reflexive, standard weighted Fock spaces $F_t^p$ to the non-reflexive cases $p = 1, \infty$. Among these results are the characterization of compactness and the Fredholm property of…

We discuss Toeplitz operators on the Segal-Bargmann space as functional realizations of anti-Wick operators on the Fock space. In the special case of radial symbols we exploit the isometric mapping between the Segal-Bargmann space and $l^2$…

In this article we study the spectrum $\sigma(T)$ and Waelbroeck spectrum $\sigma_W(T)$ of a weighted composition operator $T$ induced by a rotation on $\Hol(\D)$ and given by $$Tf(z)=m(z)f(\beta z) \ \ \ (z\in \D)$$ where $m\in \Hol(\D)$,…

We completely characterize the simultaneous membership in the Schatten ideals $S_ p$, $0<p<\infty$ of the Hankel operators $H_ f$ and $H_{\bar{f}}$ on the Bergman space, in terms of the behaviour of a local mean oscillation function,…

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 $T$ be a compact operator on a separable Hilbert space $H$. We show that, for $2\le p<\infty$, $T$ belongs to the Schatten class $S_p$ if and only if $\{\|Tf_n\|\}\in \ell^p$ for \emph{every} frame $\{f_n\}$ in $H$; and for $0<p\le2$,…

Let $A_1, ... A_n$ be operators acting on a separable complex Hilbert space such that $\sum_{i=1}^n A_i=0$. It is shown that if $A_1, ... A_n$ belong to a Schatten $p$-class, for some $p>0$, then 2^{p/2}n^{p-1} \sum_{i=1}^n \|A_i\|^p_p \leq…

In this note, we give criteria on noncommutative integral kernels ensuring that integral operators on quantum torus belong to Schatten classes. With the engagement of a noncommutative Schwartz' kernel theorem on the quantum torus, a…

For $1\le p<\infty$, let $F^p_\varphi$ be the Fock spaces on ${\mathbb C}^n$ with the weight function $\varphi$ that \(\varphi \in {\mathcal{C}}^{2}\left( {\mathbb{C}}^{n}\right)\) is real-valued and satisfies $ m{\omega }_{0} \leq…

Let $A_{\alpha}^{p}(\mathbb{B}^n;\mathbb{C}^d)$ be the weighted Bergman space on the unit ball $\mathbb{B}^n$ of $\mathbb{C}^n$ of functions taking values in $\mathbb{C}^d$. For $1<p<\infty$ let $\mathcal{T}_{p,\alpha}$ be the algebra…

In the present article, composition operators induced by Rational Inner Functions on the bidisc $\mathbb{D}^2$ are studied, acting on the weighted Bergman space $A^2_{\beta}(\mathbb{D}^2).$ We prove that under mild conditions that Rational…

The paper deals with the invertibility of Toeplitz plus Hankel operators T(a)+H(b) acting on classical Hardy spaces on the unit circle T. It is supposed that the generating functions a and b satisfy the condition a(t)a(1/t)=b(t)b(1/t).…

We characterize the compactness of composition operators; in term of generalized Nevanlinna counting functions, on a large class of Hilbert spaces of analytic functions, which can be viewed between the Bergman and the Dirichlet spaces

This paper continues the study of paragrassmann algebras begun in Part I with the definition and analysis of Toeplitz operators in the associated holomorphic Segal-Bargmann space. These are defined in the usual way as multiplication by a…

We present complete classifications of Toeplitz + Hankel operators on vector-valued Hardy spaces and classify paired operators on $L^2(\mathbb{T})$. We also study the latter class through the lens of inner functions on the disc.

We consider Toeplitz operators defined on a concave corner-shaped subset of the square lattice. We obtain a necessary and sufficient condition for these operators to be Fredholm. We further construct a Fredholm concave corner Toeplitz…

Let $\mathrm{D}^\mathrm{I}_{n \times n}$ be the Cartan domain of type I which consists of the complex $n \times n$ matrices $Z$ that satisfy $Z^*Z < I_n$. For a symbol $a \in L^\infty(\mathrm{D}^\mathrm{I}_{n \times n})$ we consider three…

In this paper we study the product of Toeplitz operators on the harmonic Bergman space of the unit disk of the complex plane C. Mainly, we discuss when the product of two quasihomogeneous Toeplitz operators is also a Toeplitz operator, and…

Compressions of Toeplitz operators to coinvariant subspaces of $H^2$ are called truncated Toeplitz operators. We study two questions related to these operators. The first, raised by Sarason, is whether boundedness of the operator implies…