Operator monotone functions induced from Löwner-Heinz inequality and strictly chaotic order

Abstract

Furuta presented direct and simplified proofs of operator monotonicity of functions φ(t) = t − 1 log t and ψ(t) = t log t − t + 1 (log t)2 by using Lowner-Heinz inequality. Extending his method, we give a sequence of operator monotone functions {f k(t)}∞k=0 with f 0(t) = φ(t) and f 1(t) = ψ(t) . We also study relations between f k(t) and strictly chaotic order defined among positive invertible operators and obtain some extensions of results due to Furuta. Mathematics subject classification (2000): 47A63.