Abstract
Let and |||.||| be a unitarily invariant norm. We introduce a log-convex (and hence a convex) function g on the interval [0, 1] such that g is decreasing on [0, 1 / 2], increasing on [1 / 2, 1] and attains its minimum at 1 / 2. Moreover,
for . Related interpolating inequalities are also proved. This implies an improvement of a recent result of Audenaert.
Disclosure statement
No potential conflict of interest was reported by the author.