Related papers: Some upper bounds for the $\mathbb{A}$-numerical r…

Consider $\mathcal{H}$ is a complex Hilbert space and $A$ is a positive operator on $\mathcal{H}.$ The mapping $\langle\cdot,\cdot\rangle_A: \mathcal{H}\times \mathcal{H} \to \mathbb {C}$, defined as $\left\langle…

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

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…

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 $A$ 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 generalize several inequalities involving powers of the numerical radius for off-diagonal part of $2\times2$ operator matrices of the form $T=\left[\begin{array}{cc} 0&B, C&0 \end{array}\right]$, where $B, C$ are two operators. In…

Let $A=[A_{ij}]$ be an $n\times n$ operator matrix where each $A_{ij}$ is a bounded linear operator on a complex Hilbert space $\mathcal{H}$. With other numerical radius bounds via contraction operators, we show that $w(A) \leq…

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…

We develop various lower bounds for the numerical radius $w(A)$ of a bounded linear operator $A$ defined on a complex Hilbert space, which improve the existing inequality $w^2(A)\geq \frac{1}{4}\|A^*A+AA^*\|$. In particular, for $r\geq 1$,…

This paper establishes new upper bounds for the $A$-numerical radius of operator matrices in semi-Hilbertian spaces by leveraging the $A$-Buzano inequality and developing refined techniques for operator matrices. We present several sharp…

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…

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…

We obtain upper bounds for the numerical radius of a product of Hilbert space operators which improve on the existing upper bounds. We generalize the numerical radius inequalities of $n\times n$ operator matrices by using non-negative…

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 $A$ 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 $w^2(A)\leq \frac12 \|A^*A+AA^*\|$,…

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…

This paper is a continuation of a recent work on a new norm, christened the $ (\alpha, \beta)$-norm, on the space of bounded linear operators on a Hilbert space. We obtain some upper bounds for the said norm of $n\times n$ operator…

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…

Let $T$ be a bounded linear operator on a complex Hilbert space $\mathscr{H}.$ We obtain various lower and upper bounds for the numerical radius of $T$ by developing the Euclidean operator radius bounds of a pair of operators, which are…

In this article, we developed a series of new inequalities involving the $q$-numerical radius for operators and $2\times 2$ operator matrices. These inequalities serve to establish both lower and upper bounds for the $q$-numerical radius of…