Best possibility of the Furuta inequality
Abstract: Let , and . Furuta (1987) proved that if bounded linear operators on a Hilbert space satisfy , then . 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 .
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Affiliation: Department of Mathematics, Tohoku College of Pharmacy, Komatsushima, Aoba-ku, Sendai 981, Japan
Keywords: The L\"owner-Heinz inequality, the Furuta inequality, positive operator
Received by editor(s): February 25, 1994
Received by editor(s) in revised form: July 7, 1994
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1996 American Mathematical Society