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A capital letter means a bounded linear operator on a Hilbert space H. The celebrated Lowner-Heinz inequality asserts that A B 0 ensures Aα Bα for any α ∈ (0,1) ,b utAp B p does not always hold for p > 1. From this point of view, we shall prove the following result. Let A B 0 with A > 0 ,t ∈ (0,1) and p1,p2,...,p2n 1 for natural number n. Then the following inequality holds for r t: A 1−t+r A r 2 A −t 2 {A t 2 ... A −t 2 A t 2 (A −t 2

Further extension of an order preserving operator inequality