Proceedings of the American Mathematical Society

Author(s): C.-S. Lin
Journal: Proc. Amer. Math. Soc. 129 (2001), 855-859.
MSC (1991): Primary 47A63
Posted: September 20, 2000
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Two of the most useful inequality formulas for bounded linear operators on a Hilbert space are the Löwner-Heinz and Reid's inequalities. The first inequality was generalized by Furuta (so called the Furuta inequality in the literature). We shall generalize the second one and obtain its related results. It is shown that these two generalized fundamental inequalities are all equivalent to one another.

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C.-S. Lin
Affiliation: Department of Mathematics, Bishop's University, Lennoxville, Quebec, Canada J1M 1Z7
Email: plin@ubishops.ca

DOI: 10.1090/S0002-9939-00-05650-1
PII: S 0002-9939(00)05650-1
Keywords: Positive operator, Hermitian operator, polar decomposition, L\"{o}wner-Heinz inequality, Reid's inequality, Furuta's inequality, contraction
Received by editor(s): May 25, 1999
Posted: September 20, 2000
Dedicated: Dedicated to Professor Jone Lin on his retirement
Communicated by: Jonathan M. Borwein
Copyright of article: Copyright 2000, American Mathematical Society

C.-S. Lin, Inequalities of Reid type and Furuta, Inequalities of Reid type and Furuta, Proceedings of the American Mathematical Society, 2001, pp. NA. (English)

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