Interpolating inequalities for unitarily invariant norms and numerical radii of matrices

Abstract

In this paper, which is a continuation of our works in [9] and [10], we prove several interpolating inequalities for norms and numerical radii of matrices. Special cases of our results present refinements of some known inequalities. Among other results, we prove that if A, B, X are n × n complex matrices such that X is positive semidefinite and t ∈ [0, 1], then