The Furuta inequality with negative powers

Tanahashi, Kôtarô

doi:10.1090/S0002-9939-99-04705-X

The Furuta inequality with negative powers
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by Kôtarô Tanahashi PDF

Proc. Amer. Math. Soc. 127 (1999), 1683-1692 Request permission

Abstract:

Let $A, B \in B(H)$ be bounded linear operators on a Hilbert space $H$ satisfying $O\leq B\leq A$. Furuta showed the operator inequality $(A^{r}B^{p}A^{r})^{\frac {1}{q}}\leq$ $A^{\frac {p+2r}{q}}$ as long as positive real numbers $p , q, r$ satisfy $p+2r\leq (1+2r)q$ and $1\leq q$. In this paper, we show this inequality is valid if negative real numbers $p, q, r$ satisfy a certain condition. Also, we investigate the optimality of that condition.

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