Some operator inequalities involving operator means and positive linear maps

Abstract

Let A and B be two positive operators with for positive real numbers be an operator mean and be the adjoint mean of If and is a positive unital linear map, then

where

and is the Kantorovich constant. In addition, for

Keywords:

• Kantorovich constant
• operator mean
• operator inequality
• positive linear map

AMS Subject Classifications:

• 46L07
• 47A63
• 47A30
• 15A60

Notes

No potential conflict of interest was reported by the authors.

Additional information

Funding

M. S. Moslehian was supported by Ferdowsi University of Mashhad [grant number 2/44453].