Related papers: Numerical Range and Compressions of the Shift

We establish new integral inequalities for the numerical radius and the operator norm of bounded linear operators on Hilbert spaces. Our results refine classical triangle-type and operator matrix inequalities by incorporating convex…

This is an expository-survey on weak stability of bounded linear operators acting on normed spaces in general and, in particular, on Hilbert spaces. The paper gives a comprehensive account of the problem of weak operator stability,…

The Berezin range of a bounded operator $T$ acting on a reproducing kernel Hilbert space $\mathcal{H}$ is the set $B(T)$ := $\{\langle T\hat{k}_{x},\hat{k}_{x} \rangle_{\mathcal{H}} : x \in X\}$, where $\hat{k}_{x}$ is the normalized…

For a wide family of multivariate Hausdorff operators, a new stronger condition for the boundedness of an operator from this family on the real Hardy space $H^1$ by means of atomic decomposition.

We investigate the generalized quadratic operator defined by $$T =\left( \begin{array}{cc} a I_H & A \\ c A^* & bI_K \end{array} \right) ,$$ where $H$ and $K$ are Hilbert spaces, $A:K\to H$ is a bounded linear operator, $I_H$ and $I_K$…

This article is about the (minimal) sector containing the numerical range of the principal part of a linear second-order elliptic differential operator defined by a form on closed subspaces V of the first-order Sobolev space…

The concepts of weighted numerical radius has been defined in recent times. In this article, we obtain several upper bound for weighted numerical radius of operators and $2 \times 2$ operator matrices which generalize and improves some well…

Several upper and lower bounds for the numerical radius of $2 \times 2$ operator matrices are developed which refine and generalize the earlier related bounds. In particular, we show that if $B,C$ are bounded linear operators on a complex…

We study the behaviour on rearrangement-invariant spaces of such classical operators of interest in harmonic analysis as the Hardy-Littlewood maximal operator (including the fractional version), the Hilbert and Stieltjes transforms, and the…

This survey aims to give a brief introduction to operator theory in the Hardy space over the bidisc $H^2(\mathbb D^2)$. As an important component of multivariable operator theory, the theory in $H^2(\mathbb D^2)$ focuses primarily on two…

Let ($\mathcal{H}, \langle . , .\rangle )$ be a complex Hilbert space and $A$ be a positive bounded linear operator on it. Let $w_A(T)$ be the $A$-numerical radius and $\|T\|_A$ be the $A$-operator seminorm of an operator $T$ acting on the…

In this paper, we show several bounds for the numerical radius of a Hilbert space operator in terms of the Euclidean operator norm. The obtained forms will enable us to find interesting refinements of celebrated results in the literature.…

In previous work, the authors studied the compressed shift operators $S_{z_1}$ and $S_{z_2}$ on two-variable model spaces $H^2(\mathbb{D}^2)\ominus \theta H^2(\mathbb{D}^2)$, where $\theta$ is a two-variable scalar inner function. Among…

Given a contraction A on a Hilbert space H, an operator T on H is said to be A-invariant if <Tx,x>=<TAx,Ax> for every x in H such that ||Ax||=||x||. In the special case in which both defect indices of A are equal to 1, we show that every…

We present some 2-isometric lifting and extension results for Hilbert space concave operators. For a special class of concave operators we study their Cauchy dual operators and discuss conditions under which these operators are subnormal.…

A conjugation $C$ on a separable complex Hilbert space $\mathcal H$ is an antilinear operator that is isometric and involutive. In this notes, we characterize all conjugations on the Hardy-Hilbert space $H^{2}$ over the disk. In addition,…

For any n-by-n complex matrix T and any $1\leqslant k\leqslant n$, let $\Lambda_{k}(T)$ the set of all $\lambda\in \C$ such that $PTP=\lambda P$ for some rank-k orthogonal projection $P$ be its higher rank-k numerical range. It is shown…

We extend results on compressed Toeplitz operators on the backward shift invariant subspaces of $H^2 $ to the context of the spaces $H^p$, $1<p<\infty.$

For a positive trace-class operator $C$ and a bounded operator $A$, we provide an explicit description of the closure of the orbit-closed $C$-numerical range of $A$ in terms of those operators submajorized by $C$ and the essential numerical…

Proper splittings of operators are commonly used to study the convergence of iterative processes. In order to approximate solutions of operator equations, in this article we deal with proper splittings of closed range bounded linear…