This paper deals with the so-called A-numerical radius associated a positive (semi-definite) bounded linear operator A acting on complex Hilbert space H. Several new inequalities involving this concept are established. In particular, we prove several estimates for 2×2 matrices whose entries A-bounded operators. Some of obtained results cover and extend well-known recent due to Bani-Domi Kittane...

If A, B are bounded linear operators on a complex Hilbert space, then we prove that $$\begin{aligned} w(A)\le & {} \frac{1}{2}\left( \Vert A\Vert +\sqrt{r\left( |A||A^*|\right) }\right) ,\\ w(AB \pm BA)\le 2\sqrt{2}\Vert B\Vert \sqrt{ w^2(A)-\frac{c^2(\mathfrak {R}(A))+c^2(\mathfrak {I}(A))}{2} }, \end{aligned}$$ where $$w(\cdot ),\left\| \cdot \right\| $$ , and $$r(\cdot )$$ the numerical radi...

Abstract In this paper, we improve some numerical radius inequalities for Hilbert space operators under suitable condition. We also compare our results with known results. As application of result, obtain an operator inequality.