### Generalizations of numerical radius inequalities related to block matrices

#### Abstract

We establish several numerical radius inequalities related to 2×2 positive semidefinite block matrices. It is shown that if A,B,C∈[M]<LaTeX>\mathbb{M}</LaTeX>_{n}(ℂ) are such that [

A B^{∗}

B C

]≥0, then

w^{r}(B)≤(1/2)w(A^{r}+C^{r}), for r≥1.

Related numerical radius inequalities for sums and products of matrices are also given.

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