Related papers: New Estimates for the Numerical Radius

In the infinite-dimensional separable complex Hilbert space we construct new abstract examples of unbounded maximal accretive and maximal sectorial operators $B$ for which ${\rm dom\,}B^{\frac{1}{2}}\ne{\rm dom\,}B^{*{\frac{1}{2}}}$. New…

This paper introduces and investigates the concept of the $q$-numerical range for tuples of bounded linear operators in Hilbert spaces. We establish various inequalities concerning the $q$-numerical radius associated with these operator…

In this paper we give several expressions of spectral radius of a bounded operator on a Hilbert space, in terms of iterates of Aluthge transformation, numerical radius and the asymptotic behavior of the powers of this operator. Also we…

Here, we study the $q$-numerical radius of rank-one operators on a Hilbert space $\mathcal{H}$. More precisely, for $q \in [0,1]$ and $a, b \in \mathcal{H}$, we establish the formula \[ \omega_q(a \otimes b) = \frac{1}{2}\left(\|a\|\|b\| +…

Let $T$ be an operator on a Hilbert space $H$ with numerical radius $w(T)\le1$. According to a theorem of Berger and Stampfli, if $f$ is a function in the disk algebra such that $f(0)=0$, then $w(f(T))\le\|f\|_\infty$. We give a new and…

In this paper, we introduce a new semi-norm of operators on a semi-Hilbertian space, which generalizes the A-numerical radius and A-operator semi-norm. We study the basic properties of this semi-norm, including upper and lower bounds for…

We present new bounds for the numerical radius of bounded linear operators and $2\times 2$ operator matrices. We apply upper bounds for the numerical radius to the Frobenius companion matrix of a complex monic polynomial to obtain new…

Let $D$ be an invertible multiplication operator on $L^2(X, \mu)$, and let $A$ be a bounded operator on $L^2(X, \mu)$. In this note we prove that $\|A\|^2 \le \|D A\| \, \|D^{-1} A\|$, where $\|\cdot\|$ denotes the operator norm. If, in…

We introduce a new seminorm of $n$-tuple operators, which generalizes the $A$-Euclidean operator radius of $n$-tuple bounded linear operators on a complex Hilbert space. We introduce and study basic properties of this seminorm. As an…

The main goal of this article is to establish several new $\mathbb{A}$-numerical radius equalities and inequalities for $n\times n$ cross-diagonal, left circulant, skew left circulant operator matrices, where $\mathbb{A}$ is the $n\times n$…

Let $\mathbb{A}=\left( \begin{array}{cc} A & 0 \\ 0 & A \\ \end{array} \right)$ be the $2\times2$ diagonal operator matrix determined by a positive bounded operator $A$. For semi-Hilbertian operators $X$ and $Y$, we first show that…

Let $A$ be a bounded linear positive operator on a complex Hilbert space $\mathcal{H}.$ Further, let $\mathcal{B}_A\mathcal{(H)}$ denote the set of all bounded linear operators on $\mathcal{H}$ whose $A$-adjoint exists, and $\mathbb{A}$…

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)…

Some new trace inequalities for operators in Hilbert spaces are provided. The superadditivity and monotonicity of some associated functionals are investigated and applications for power series of such operators are given. Some trace…

In this article, we proved upper bounds for numerical radius of bounded linear operator and product of operators which generalize and improve existing inequalities. We also obtain a numerical radius inequality of invertible operator using…

Let $A$ be a positive bounded operator on a Hilbert space $\big(\mathcal{H}, \langle \cdot, \cdot\rangle \big)$. The semi-inner product ${\langle x, y\rangle}_A := \langle Ax, y\rangle$, $x, y\in\mathcal{H},$ induces a seminorm…

In this paper, we study the relationship between operator space norm and operator space numerical radius on the matrix space $\mathcal{M}_n(X)$, when $X$ is a numerical radius operator space. Moreover, we establish several inequalities for…

This paper investigates new properties of $q$-numerical ranges for compact normal operators and establishes refined upper bounds for the $q$-numerical radius of Hilbert space operators. We first prove that for a compact normal operator $T$…

Let $\mathcal{A}$ be a unital $\mathbf{C}^*$-algebra with unit $e$. We develop several inequalities for a positive linear functional $f$ on $\mathcal{A}$ and obtain several bounds for the numerical radius $v(a)$ of an element $a\in…