Positive definiteness and infinite divisibility of certain functions of hyperbolic cosine function

Abstract

Positive definiteness and infinite divisibility of certain functions of [Formula: see text] (explained in the introduction) are studied. Criterion of positive definiteness is useful to study certain norm comparison results for operator means.

Wigner--Yanase--Dyson function and logarithmic mean

“…The set M + (n, C) represents all positive semi-definite matrices in M (n, C). The stronger ordering N 1 (x, y) N 2 (x, y) for means N 1 and N 2 have been studied in [3,7,8,11,14] for the study of the unitarily invariant norm inequalities and recent advances on the related topics.…”