Characterization of mean transformations

Abstract

The mean transformations M(A, B) are linear mappings and they are analogues of the matrix means of A, B ≥ 0. They are defined by operator monotone functions. In this article several properties are described and a part of them characterize the concept.

Keywords:

• matrix monotone function
• matrix means
• transformer inequality
• trace-preserving mappings

AMS Subject Classifications::

• Primary: 26E60
• Secondary: 15A45