Related papers: Minimal norm Hankel operators

We provide a number of sharp inequalities involving the usual operator norms of Hilbert space operators and powers of the numerical radii. Based on the traditional convexity inequalities for nonnegative real numbers and some generalize…

The Hardy operator $T_a$ on a tree $\G$ is defined by \[(T_af)(x):=v(x) \int^x_a u(t)f(t) dt \qquad {for} a, x\in \G. \] Properties of $T_a$ as a map from $L^p(\G)$ into itself are established for $1\le p \le \infty$. The main result is…

Let $M$ be a closed spin manifold and let $N$ be a closed manifold. For maps $f\colon M\to N$ and Riemannian metrics $g$ on $M$ and $h$ on $N$, we consider the Dirac operator $D^f_{g,h}$ of the twisted Dirac bundle $\Sigma…

The Carleman operator is defined as integral operator with kernel $(t+s)^{-1}$ in the space $L^2 ({\Bbb R}_{+}) $. This is the simplest example of a Hankel operator which can be explicitly diagonalized. Here we study a class of self-adjoint…

In this paper, we identify a large class of hyponormal block Toeplitz operators whose self-commutators are of finite rank. \ Recall that an operator $T_\varphi$ is hyponormal and $[T_\varphi^{*}, T_\varphi]$ is a finite rank operator if and…

The aim of this paper is to characterize the nonnegative functions $\varphi$ defined on $(0,\infty)$ for which the Hausdorff operator $$\mathscr H_\varphi f(z)= \int_0^\infty f\left(\frac{z}{t}\right)\frac{\varphi(t)}{t}dt$$ is bounded on…

We will show that a theorem of Rudin \cite{wr1}, \cite{wr}, permits us to determine minimal projections not only with respect to the operator norm but with respect to quasi-norms in operators ideals and numerical radius in many concrete…

We consider kernels of unbounded Toeplitz operators in $H^p(\mathbb C^+)$ in terms of a factorization of their symbols. We study the existence of a minimal Toeplitz kernel containing a given function in $H^p(\mathbb C^+)$, we describe the…

Let $f$ be a symmetric norm on ${\mathbb R}^n$ and let ${\mathcal B}({\mathcal H})$ be the set of all bounded linear operators on a Hilbert space ${\mathcal H}$ of dimension at least $n$. Define a norm on ${\mathcal B}({\mathcal H})$ by…

We prove a Strong Haagerup inequality with operator coefficients. If for an integer d, H_d denotes the subspace of the von Neumann algebra of a free group F_I spanned by the words of length d in the generators (but not their inverses), then…

Let $G=(V,E)$ be a finite graph and $M_G$ be the centered Hardy-Littlewood maximal operator defined there. We find the optimal value $\bf{C}_{G,p}$ such that the inequality $$\text{Var}_{p}(M_{G}f)\leq {\textbf{C}}_{G,p}\text{Var}_{p}(f)$$…

Generalization of functions of bounded mean oscillation and Hankel operators to the case of compact abelian groups with linearly ordered dual is considered. Spaces of functions of bounded mean oscillation and of bounded mean oscillation of…

A simple normal form for Hardy operators is introduced that unifies and simplifies the theory of weighted Hardy inequalities. A straightforward transition to normal form is given that applies to the various Hardy operators and their duals,…

In this article, we characterize absolutely norm attaining normal operators in terms of the essential spectrum. Later we prove a structure theorem for hyponormal absolutely norm attaining (or $\mathcal{AN}$-operators in short) and deduce…

Let $L$ be a one-to-one operator of type $\omega$ having a bounded $H_\infty$ functional calculus and satisfying the $k$-Davies-Gaffney estimates with $k\in{\mathbb N}$. In this paper, the authors introduce the weak Hardy space…

We study hypercyclicity of the Toeplitz operators in the Hardy space $H^2(\mathbb{D})$ with symbols of the form $p(\bar{z}) +\phi(z)$, where $p$ is a polynomial and $\phi \in H^\infty(\mathbb{D})$. We find both necessary and sufficient…

Motivated by a recent study of Bessel operators in connection with a refinement of Hardy's inequality involving $1/\sin^2(x)$ on the finite interval $(0,\pi)$, we now take a closer look at the underlying Bessel-type operators with more…

We consider the remaining unsettled cases in the problem of existence of energy minimizing solutions for the Dirichlet value problem $L_\gamma u-\lambda u=\frac{u^{2^*(s)-1}}{|x|^s}$ on a smooth bounded domain $\Omega$ in $\mathbb{R}^n$…

The norm of $C-I$ on $\ell^p$, where $C$ is the Ces\`aro operator, is shown to be $1/(p-1)$ when $1<p\le2$. This verifies a recent conjecture of G. J. O. Jameson. The norm of $C-I$ on $\ell^p$ is also determined when $2< p<\infty$. The two…

We consider random linear continuous operators $\Omega \to \mathcal{L}(\mathcal{H}, \mathcal{H})$ on a Hilbert space $\mathcal{H}$. For example, such random operators may be random quantum channels. The Central Limit Theorem is known for…