A new characterization of the operator perspective

Abstract

In this paper, we give a new characterization for the perspective of a continuous function under certain assumptions. This result generalizes a non-commutative analogue of the arithmetic–geometric mean inequality. Our main result extends and strengthens the existing result concerning the characterization of the geometric operator mean. We provide the characterization of other operator means, in particular, the harmonic operator mean and the arithmetic operator mean.

Keywords:

• Operator inequality
• geometric operator mean
• arithmetic operator mean
• harmonic operator mean
• operator perspective

2010 Mathematics Subject Classifications:

• Primary 47A63
• Secondary 46L05
• 46L60

Acknowledgments

The author thanks the referee for the careful and expert reading of the manuscript, and for the clever remarks and pertinent suggestions that led to a substantial improvement of the presentation.

Disclosure statement

No potential conflict of interest was reported by the author(s).