Some inequalities for the numerical radius and spectral norm for operators in Hilbert C^-modules space

In this paper, a fresh approach to investigating the numerical radius of bounded operators on Hilbert C^*-modules is presented. By using our approach, we can produce some novel findings and extend certain established theorems for bounded adjointable operators on Hilbert C^*-module spaces. Moreover, we find an upper bound for power of the numerical radius of t^ys^1-under assumption 0 1. In fact, we prove wct^^{1-} yʳ t^r+ (1-) s^{r}for all 0 1 and r 2.