Inequalities of Reid type and Furuta
Author:
C.S. Lin
Journal:
Proc. Amer. Math. Soc. 129 (2001), 855859
MSC (1991):
Primary 47A63
Published electronically:
September 20, 2000
MathSciNet review:
1709759
Fulltext PDF Free Access
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Abstract: Two of the most useful inequality formulas for bounded linear operators on a Hilbert space are the LöwnerHeinz 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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Additional Information
C.S. Lin
Affiliation:
Department of Mathematics, Bishop’s University, Lennoxville, Quebec, Canada J1M 1Z7
Email:
plin@ubishops.ca
DOI:
http://dx.doi.org/10.1090/S0002993900056501
PII:
S 00029939(00)056501
Keywords:
Positive operator,
Hermitian operator,
polar decomposition,
L\"{o}wnerHeinz inequality,
Reid's inequality,
Furuta's inequality,
contraction
Received by editor(s):
May 25, 1999
Published electronically:
September 20, 2000
Dedicated:
Dedicated to Professor Jone Lin on his retirement
Communicated by:
Jonathan M. Borwein
Article copyright:
© Copyright 2000
American Mathematical Society
