Upper bounds for numerical radius inequalities involving off-diagonal operator matrices

Abstract

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 $T=\left[\begin{array}{ccc}0& X,Y& 0\end{array}\right]$, then \begin{align*} ω^{r}(T)\leq 2^{r-2}\left\|f^{2r}(|X|)+g^{2r}(|Y^*|)\right\|^\frac{1}{2}\left\|f^{2r}(|Y|)+g^{2r}(|X^*|)\right\|^\frac{1}{2} \end{align*} and \begin{align*} ω^{r}(T)\leq 2^{r-2}\left\|f^{2r}(|X|)+f^{2r}(|Y^*|)\right\|^\frac{1}{2}\left\|g^{2r}(|Y|)+g^{2r}(|X^*|)\right\|^\frac{1}{2}, \end{align*} where $X,Y$ are bounded linear operators on a Hilbert space $\mathcal{H}$, $r\ge 1$ and $f$, $g$ are nonnegative continuous functions on $[0,\infty )$ satisfying the relation $f(t)g(t)=t(t\in [0,\infty ))$. Moreover, we present some inequalities involving the generalized Euclidean operator radius of operators $T_1,\cdots ,T_n$.

References in corpus (1)

• Extension of Euclidean operator radius inequalities

Cited by in corpus (4)

• On A-numerical radius inequalities for $2\times 2$ operator matrices
• Characterization of numerical radius parallelism in $C^{\ast }$-algebras
• On $\mathbb{A}$-numerical radius inequalities for $2\times 2$ operator matrices-II
• Sharp inequalities for the numerical radius of block operator matrices