Related papers: Numerical radius inequalities for Hilbert Space Op…
Recently proved weighted Cauchy Scwarz inequality for Hilbert $C^*$-modules leads to many H\"older type inequalities for unitarily invariant norms on Hilbert space operators.
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 prove several singular value inequalities for sum and product of compact operators in Hilbert space. Some of our results generalize the previous inequalities for operators. Also, applications of some inequalities are given.
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…
New upper and lower bounds for the numerical radii of Hilbert space operators are given. Among our results, we prove that if $A\in \mathcal{B} \left( \mathcal{H}\right) $ is a hyponormal operator, then for all non-negative non-decreasing…
This article implements a simple convex approach and block techniques to obtain several new refined versions of numerical radius inequalities for Hilbert space operators. This includes comparisons among the norms of the operators, their…
Employing the Orlicz functions we extend the Buzano's inequality which is a refinement of the Cauchy-Schwarz inequality. Also using the Orlicz functions we obtain several numerical radius inequalities for a bounded linear operator as well…
Several numerical radius inequalities are studied by developing an extension of the Buzano's inequality. It is shown that if $T$ is a bounded linear operator on a complex Hilbert space, then \begin{eqnarray*} w^n(T) &\leq& \frac{1}{2^{n-1}}…
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 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…
The H$\ddot{{\rm o}}$lder-McCarty inequalities are originally derived in the Hilbert space case and have been generalized via a convex inequality. The main purpose of this paper is to extend this convex inequality to the Hilbert…
We develop a number of inequalities to obtain bounds for the numerical radius of a bounded linear operator defined on a complex Hilbert space using the properties of $t$-Aluthge transform. We show that the bounds obtained are sharper than…
In this article, we employ certain properties of the transform $C_{M,m}(A)=(MI-A^*)(A-mI)$ to obtain new inequalities for the bounded linear operator $A$ on a complex Hilbert space $\mathcal{H}$. In particular, we obtain new relations among…
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…
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…
In this paper, the $q$-numerical radius of operators in semi-Hilbertian spaces is studied. New characterizations are established, and sharp upper and lower bounds for the $q$-numerical radius are derived. Moreover, several inequalities…
In this paper, we establish some upper bounds for numerical radius inequalities including of $2\times 2$ operator matrices and their off-diagonal parts. Among other inequalities, it is shown that if $T=\left[\begin{array}{cc} 0&X, Y&0…
We give some new refinements of Heinz inequality and an improvement of the reverse Young's inequality for scalars and we use them to establish new inequalities for operators and the Hilbert-Schmidt norm of matrices. We give a uniformly and…
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…
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…