New norm and numerical radius bounds

Finding new bounds for norms and the numerical radius of certain matrix forms is a renowned topic that has attracted numerous researchers. In this paper, we show some new bounds for unitarily invariant norms and the numerical radius of certain matrix forms that involve products of matrices and sums of products. New arithmetic-geometric mean-type inequalities and a refinement of the celebrated Cauchy–Schwarz inequality are shown among the obtained results. Our results are compared with those in the literature through numerical examples and rigorous approaches.