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 L(A, B) ≥ L( A, B), where L(A, B) is the logarithmic mean of A and B, and A means the real part of A. This complements a recent result of Lin and Sun.

Some norm inequalities for upper sector matrices

“…As 0 S α , then A is nonsingular. Some recent studies of sector matrices can be found in [6,12,[14][15][16][17]. Recent research interest in this class of matrices starts with a resolution of a problem from numerical analysis [3].…”

Numerical radii of accretive matrices

“…This definition was motivated by the same definition for positive matrices, and many properties of operator mean of accretive matrices were given in [5]. In [21], the logarithmic mean of accretive A, B is defined by…”