IJPAM: Volume 62, No. 3 (2010)

GENERALIZATION OF $\beta $-POWER-MEAN
FOR OPERATORS

C.-S. Lin
Department of Mathematics
Bishop's University
2600, College Street, Sherbrooke, QC, J1M 1Z7, CANADA
e-mail: [email protected]


Abstract.Motivated by Hayashi's mapping and characterization of $r$-mean [3], we present a generalization of the mapping and the $\beta $-power-mean which was originated in [4]. Instead of two operators we generalize the $\beta $-power-mean to $2n+1$ operators. Some applications are given about the Furuta-type operator inequalities.


Dedicated to Professor Showhwa Lin
with admiration and respects.


Received: May 25, 2010

AMS Subject Classification: 47A63

Key Words and Phrases: $r$-mean, $\alpha $-power-mean, $\beta $-power mean, grand Furuta ineauality, Furuta's further extension of operator inequality, log majorization.

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2010
Volume: 62
Issue: 3