# 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: and the -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.