We utilize some $2 \\times 2$ matrix tricks to obtain several unitarily invariant norm inequalities corresponding to the L\\"{o}wner--Heinz inequality, the arithmetic--geometric mean inequality and the Corach--Porta--Recht inequality...

We prove some refinements of an inequality due to X. Zhan in an arbitrary complex Hilbert space by using some results on the Heinz inequality. We present several related inequalities as well as new variants of the Corach--Porta--Recht inequality. We...