On the logarithmic mean of accretive matrices

Abstract

In this paper, we define the logarithmic mean of two accretive matrices and study its basic properties. Among other results, we show that if A; B are accretive matrices, then RL(A,B) ? L(RA,RB), where L(A,B) is the logarithmic mean of A and B, and RA means the real part of A. This complements a recent result of Lin and Sun.