- Hacettepe Journal of Mathematics and Statistics
- Vol: 48 Issue: 4
- Some generalized numerical radius inequalities involving Kwong functions
Some generalized numerical radius inequalities involving Kwong functions
Authors : Mojtaba Bakherad
Pages : 951-958
View : 10 | Download : 5
Publication Date : 2019-08-08
Article Type : Research
Abstract :We prove several numerical radius inequalities involving positive semidefinite matrices via the Hadamard product and Kwong functions. Among other inequalities, it is shown that if $X$ is an arbitrary $n\times n$ matrix and $A,B$ are positive semidefinite, then \[ \omega(H_{f,g}(A))\leq k\, \omega(AX+XA), \] which is equivalent to \[\omega\big(H_{f,g}(A,B)\pm H_{f,g}(B,A)\big)\leq k'\,\left\{\omega((A+B)X+X(A+B))+\omega((A-B)X-X(A-B))\right\},\] where $f$ and $g$ are two continuous functions on $(0,\infty)$ such that $h(t)={f(t)\over g(t)}$ is Kwong, $k=\max\left\{{f(\lambda)g(\lambda)\over \lambda}: {\lambda\in\sigma(A)}\right\}$ and $k'=\max\left\{{f(\lambda)g(\lambda)\over \lambda}: {\lambda\in\sigma(A)\cup\sigma(B)}\right\}$.Keywords : numerical radius, Hadamard product, operator monotone, Kwong function