IJPAM: Volume 68, No. 2 (2011)

ON COUNTABLE SETS OF ORDER PRESERVING
OPERATOR INEQUALITIES IN HILBERT SPACES
C.-S. Lin
Department of Mathematics
Bishop's University
2600 College Street, Sherbrooke, QC, J1M 1Z7, CANADA
e-mail: plin@ubishops.ca

Abstract. In this paper we show that the well-known Furuta inequality can be expressed in countable sets of operator inequalities in two forms: $(YXY)^\beta $ and the $\beta $-power-mean. So are the ground Furuta inequality and its generalization, and the chaotic order for two operators. Generally speaking, each Furuta-type operator inequality has such expression, and they are equivalent to one another, indeed.

Received: December 3, 2010
AMS Subject Classification: 47A63, 47A6
Key Words and Phrases: Hilbert space, positive operator, $\beta $-power-mean, the operator expansion of the form $(YXY^{*})^\beta$, Furuta inequality, grand Furuta inequality and its generalization, and chaotic order for two operators

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2011
Volume: 68
Issue: 2