Abstract: The relationship between two existing Hölder inequalities of unitary invariant norms for matrices is discussed. Meanwhile, we present some inequalities of unitarily invariant norms for matrices by using Hölder inequality of unitary invariant norms for matrices and some existing inequalities of unitary invariant norms. Our results are generalizations or refinements of ones shown Alakhrass and Lee.

Key words: Unitarily invariant norms, Hölder inequality, Operator convex functions, Operator concave functions