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Best possibility of the Furuta inequality

Authors:	Kô tarô Tanahashi

Affiliation:	Department of Mathematics, Tohoku College of Pharmacy, Komatsushima, Aoba-ku, Sendai 981, Japan

Abstract:	Let , and . Furuta (1987) proved that if bounded linear operators on a Hilbert space satisfy , then $(A^r B^p A^r)^{1/q} le A^{(p+2r)/q}$ . In this paper, we prove that the range and is best possible with respect to the Furuta inequality, that is, if or , then there exist which satisfy but $(A^r B^p A^r)^{1/q}nleq A^{(p+2r)/q}$ .

Keywords:	The L" owner-Heinz inequality, the Furuta inequality, positive operator

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