Related papers: Numerical radius and distance from unitary operato…

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…

In this article, we present some new general forms of numerical radius inequalities for Hilbert space operators. The significance of these inequalities follow from the way they extend and refine some known results in this field. Among other…

We obtain new lower and upper bounds for the numerical radius of a bounded linear operator $A$ on a complex Hilbert space, which refine the existing ones. In particular, if $w(A)$ and $\|A\|$ denote the numerical radius and operator norm of…

If $A,B$ are bounded linear operators on a complex Hilbert space, then % $w(A) \leq \frac{1}{2}\left( \|A\|+\sqrt{r\left(|A||A^*|\right)}\right)$ and $w(AB \pm BA)\leq 2\sqrt{2}\|B\|\sqrt{ w^2(A)-\frac{c^2(\Re (A))+c^2(\Im (A))}{2} },$…

We obtain various upper bounds for the numerical radius $w(T)$ of a bounded linear operator $T$ defined on a complex Hilbert space $\mathcal{H}$, by developing the upper bounds for the $\alpha$-norm of $T$, which is defined as…

Using the polar decomposition of a bounded linear operator $A$ defined on a complex Hilbert space, we obtain several numerical radius inequalities of the operator $A$, which generalize and improve the earlier related ones. Among other…

Let $A$ be a bounded linear operator on a complex Hilbert space and $\Re(A)$ ( $\Im(A)$ ) denote the real part (imaginary part) of A. Among other refinements of the lower bounds for the numerical radius of $A$, we prove that…

We develop upper and lower bounds for the numerical radius of $2\times 2$ off-diagonal operator matrices, which generalize and improve on the existing ones. We also show that if $A$ is a bounded linear operator on a complex Hilbert space…

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…

Let $A$ be a bounded linear operator defined on a complex Hilbert space and let $|A|=(A^*A)^{1/2}$ be the positive square root of $A$. Among other refinements of the well known numerical radius inequality $w^2(A)\leq \frac12 \|A^*A+AA^*\|$,…

We obtain several sharp lower and upper bounds for the Euclidean operator radius of a pair of bounded linear operators defined on a complex Hilbert space. As applications of these bounds we deduce a chain of new bounds for the classical…

Let $\sigma(A)$, $\rho(A)$ and $r(A)$ denote the spectrum, spectral radius and numerical radius of a bounded linear operator $A$ on a Hilbert space $H$, respectively. We show that a linear operator $A$ satisfying $$\rho(AB)\le r(A)r(B)…

Let $A$ be a positive operator on a complex Hilbert space $\mathcal{H}.$ We present inequalities concerning upper and lower bounds for $A$-numerical radius of operators, which improve on and generalize the existing ones, studied recently in…

Several refinements of norm and numerical radius inequalities of bounded linear operators on a complex Hilbert space are given. In particular, we show that if $A$ is a bounded linear operator on a complex Hilbert space, then $$…

New inequalities for the numerical radius of bounded linear operators defined on a complex Hilbert space $\mathcal{H}$ are given. In particular, it is established that if $T$ is a bounded linear operator on a Hilbert space $\mathcal{H}$…

Some elementary inequalities providing upper bounds for the difference of the norm and the numerical radius of a bounded linear operator on Hilbert spaces under appropriate conditions are given.

For a given bounded positive (semidefinite) linear operator $A$ on a complex Hilbert space $\big(\mathcal{H}, \langle \cdot\mid \cdot\rangle \big)$, we consider the semi-Hilbertian space $\big(\mathcal{H}, \langle \cdot\mid \cdot\rangle_A…

Given a Hilbert module $H$ over a $C^*$-algebra, let $\mathcal{L}(H)$ be the set of all adjointable operators on $H$. For each $T\in\mathcal{L}(H)$, its numerical radius is defined by $w(T)=\sup\big\{\|\langle Tx, x \rangle\|: x\in H,…

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…

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…