JIPAM

Reverse Inequalities on Chaotically Geometric Mean via Specht Ratio, II  
 
  Authors: Masatoshi Fujii, Jadranka Micic, Josip E. Pecaric, Yuki Seo,  
  Keywords: Operator concavity, Power mean, Arithmetic mean, Geometric mean.  
  Date Received: 24/01/03  
  Date Accepted: 05/03/03  
  Subject Codes:

47A30, 47A63.

 
  Editors: Saburou Saitoh,  
 
  Abstract:

In 1967, as a converse of the arithmetic-geometric mean inequality, Mond and Shisha gave an estimate of the difference between the arithmtic mean and the geometric one, which we call it the Mond-Shisha difference. As an application of Mond-Pecaric method, we show some order relations between the power means of positive operators on a Hilbert space. Among others, we show that the upper bound of the difference between the arithmetic mean and the chaotically geometric one of positive operators coincides with the Mond-Shisha difference. ;



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