Related papers: The Norm of a Truncated Toeplitz Operator
We generalize recent results of Fleeman and Liaw on the topic of hyponormal Toeplitz operators acting on the Bergman space of the unit disk.
This research investigates the relations between the fixed points of asymptotically contractive operators defined on complete liner metric spaces, in general, and in separable Hilbert spaces in particular and their obtained truncations of…
We consider a class of second order degenerate kinetic operators $\mathscr{L}$ in the framework of special relativity. We first describe $\mathscr{L}$ as an H\"ormander operator which is invariant with respect to Lorentz transformations.…
We discuss the range spaces of Toeplitz operators with co-analytic symbols where we focus on the boundary behavior of the functions in these spaces as well as a natural orthogonal decomposition of this range.
The Haraux function is an important tool in monotone operator theory and its applications. One of its salient properties for a maximally monotone operator is to be valued in $[0,+\infty]$ and to vanish only on the graph of the operator.…
We study Birkhoff-James orthogonality of compact (bounded) linear operators between Hilbert spaces and Banach spaces. Applying the notion of semi-inner-products in normed linear spaces and some related geometric ideas, we generalize and…
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…
A well known result of C. Cowen states that, for a symbol $\varphi \in L^{\infty }, \; \varphi \equiv \bar{f}+g \;\;(f,g\in H^{2})$, the Toeplitz operator $T_{\varphi }$ acting on the Hardy space of the unit circle is hyponormal if and only…
Let $A_r=\{r<|z|<1\}$ be an annulus. We consider the class of operators $\mathcal{F}_r:=\{T\in\mathcal{B}(H): r^2T^{-1}(T^{-1})^*+TT^*\le r^2+1,\hspace{0.08 cm}\sigma(T)\subset A_r\}$ and show that for every bounded holomorphic function…
By establishing some reproducing kernel estimates, we characterize the bounded, compact and Schatten $p$-class Toeplitz operators with positive measure symbols on the weighted Fock space $F^2_{\alpha,w}$ for $p\geq1$, where $w$ is a weight…
We investigate the commutant problem for Toeplitz operators on the Bergman space of the unit disk whose symbols belong to a subclass of biharmonic functions. We obtain a complete characterization of when two such Toeplitz operators commute.…
In this paper we completely characterize the norm attainment set of a bounded linear operator on a Hilbert space. This partially answers a question raised recently in [\textit{D. Sain, On the norm attainment set of a bounded linear…
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.
The goal of this note is to establish non-tangential convergence results for Schr\"{o}dinger operators along restricted curves. We consider the relationship between the dimension of this kind of approach region and the regularity for the…
We study the boundedness of Toeplitz-type operators defined in the context of the Calder\'on reproducing formula considering the specific wavelets whose Fourier transforms are related to Laguerre polynomials. Some sufficient conditions for…
In this article we consider the generalized integral operators acting on the Hilbert space $H^2$. We characterize when these operators are uniform, strong and weakly asymptotic Toeplitz and Hankel operators. Moreover we completely describe…
In this paper, we present intriguing findings that characterize both the closed (unbounded) and bounded EP operators on Hilbert spaces. Additionally, we demonstrate the result $\gamma(T) \leq r(T)$, where $T$ is a bounded EP operator, and…
In this note we prove that if a sublinear operator T satisfies a certain weighted estimate in the $L^{p}(w)$ space for all $w\in A_{p}$, $1<p<+\infty$, then the operator norm of T on $L^{p}(w)$ is a continuous function of the weight $w$,…
In this paper, we continue Curto-Hwang-Lee's work to study the connection between hyponormality and subnormality for block Toeplitz operators acting on the vector-valued Hardy space of the unit circle. Curto-Hwang-Lee's work focuses…
We consider Toeplitz operators in the Fock space, under rather general conditions imposed on the symbols. It is proved that if the operator has finite rank and the symbol is a function then the operator and the symbol should be zero. The…