IJPAM: Volume 12, No. 1 (2004)
INEQUALITIES IN HILBERT SPACES
Department of Mathematics
Bishop's University
Lennoxville, Quebec, J1M 1Z7, CANADA
e-mail: plin@ubishops.ca
on his retirement.
Abstract.In this article we present some new inequalities in a Hilbert space which
are equivalent to the Cauchy-Schwarz inequality. Altered forms of
inequalities are given, and we provide necessary and sufficient conditions
for equalities. In applications these inequalities will be used to obtain
some inequalities of bounded linear operators (some of them are known) on a
Hilbert space with considerable simplifications in the proofs.
Received: January 15, 2004
AMS Subject Classification: 47A63
Key Words and Phrases: Cauchy-Schwarz inequality, Bessel inequality, polar decomposition of an operator, Heinz inequality, Löwner-Heinz formula, Furuta inequality
Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2004
Volume: 12
Issue: 1
