相关论文: Numerical radius inequalities of $2 \times 2$ oper…
Researchers have identified complex matrices $A$ such that a bounded linear operator $B$ acting on a Hilbert space will admit a dilation of the form $A \otimes I$ whenever the numerical range inclusion relation $W(B) \subseteq W(A)$ holds.…
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 develop a new refinement of the Kato's inequality and using this refinement we obtain several upper bounds for the numerical radius of a bounded linear operator as well as the product of operators, which improve the well known existing…
Denote by w(A) the numerical radius of a bounded linear operator A acting on Hilbert space. Suppose that A is invertible and that the numerical radius of A and of its inverse are no greater than 1+e for some non-negative e. It is shown that…
In this paper, we present several new bounds for the norm and numerical radius of sums of Hilbert space operators. The obtained bounds form a new collection that enriches our understanding of these bounds. We compare our bounds with the…
We develop several Euclidean operator radius bounds for the product of two $d$-tuple operators using positivity criteria of a $2\times 2$ block matrix whose entries are $d$-tuple operators. From these bounds, by using the polar…
Let $\big(\mathcal{H}, \langle \cdot\mid \cdot\rangle \big)$ be a complex Hilbert space and $A$ be a positive (semidefinite) bounded linear operator on $\mathcal{H}$. The semi-inner product induced by $A$ is given by ${\langle x\mid…
Let $A$ be a non-zero positive bounded linear operator on a complex Hilbert space $(\mathcal{H},\langle\cdot,\cdot\rangle)$. Let $\omega_A(T)$ denote the $A$-numerical radius of an operator $T$ acting on the semi-Hilbert space…
We develope new lower bounds for the $A$-numerical radius of semi-Hilbertian space operators, and applying these bounds we obtain upper bounds for the $A$-numerical radius of the commutators of operators. The bounds obtained here improve on…
In this paper, we aim to introduce and characterize the concept of numerical radius orthogonality of operators on a complex Hilbert space $\mathcal{H}$ which are bounded with respect to the semi-norm induced by a positive operator $A$ on…
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…
We obtain bounds for the numerical radius of $2 \times 2$ operator matrices which improve on the existing bounds. We also show that the inequalities obtained here generalize the existing ones. As an application of the results obtained here…
In this article, we present new inequalities for the numerical radius of the sum of two Hilbert space operators. These new inequalities will enable us to obtain many generalizations and refinements of some well known inequalities, including…
We give an alternative lower bound for the numerical radii of Hilbert space operators. As a by-product, we find conditions such that \begin{equation*} \omega\left(\left[\begin{array}{cc} 0 & R \\ S & 0 \end{array}\right]\right)=\frac{\Vert…
We introduce a numerical radius operator space $(X, \mathcal{W}_n)$. The conditions to be a numerical radius operator space are weaker than the Ruan's axiom for an operator space $(X, \mathcal{O}_n)$. Let $w(\cdot)$ be the numerical radius…
In this work, some generalizations and refinements inequalities for numerical radius of the product of Hilbert space operators are proved. New inequalities for numerical radius of block matrices of Hilbert space operators are also…
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…
Several new improvements of the $A$-numerical radius inequalities for operators acting on a semi-Hilbert space, i.e., a space generated by a positive operator $A$, are proved. In particular, among other inequalities, we show that…
We generalize several inequalities involving powers of the numerical radius for product of two operators acting on a Hilbert space. For any $A, B, X\in \mathbb{B}(\mathscr{H})$ such that $A,B$ are positive, we establish some numerical…
New inequalities for the $A$-numerical radius of the products and sums of operators acting on a semi-Hilbert space, i.e. a space generated by a positive semidefinite operator $A$, are established. In particular, it is proved for operators…