$A \geq B \geq 0$ Assures $(B^r A^p B^r)^{1/q} \geq B^{(p+2r)/q$ for $r \geq 0$, $p \geq 0$, $q \geq 1$ with $(1 + 2r)q \geq p + 2r$

Abstract

Takayuki Furuta, A ≥ B ≥ 0 Assures (Br Ap Br)1/q ≥ B^{(p+2r)/q for r ≥ 0, p ≥ 0, q ≥ 1 with (1 + 2r)q ≥ p + 2r, Proceedings of the American Mathematical Society, Vol. 101, No. 1 (Sep., 1987), pp. 85-88