AN OPERATOR INEQUALITY IMPLYING CHAOTIC ORDER

This paper proves the assertion that if positive invertible operators A and B satisfy an operator inequality (B^(t/2) A^((S-t)/2) B^(S-t) A^((S-t)/2) B^(t/2) )^(1/(2s-t))  B for 0 < t 2 – t.If s 2+t is additionally assumed then A  B. A preliminary result Theorem 2 of J.J Fuji, M. Fuji and R. Nakamoto (FFN)[1] is further generalized in Theorem 3.