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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Heinz's inequality and Bernstein's inequality


Author: C.-S. Lin
Journal: Proc. Amer. Math. Soc. 125 (1997), 2319-2325
MSC (1991): Primary 47A30, 65F15; Secondary 65J10
MathSciNet review: 1376997
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Abstract: The purpose of the present account is to sharpen Heinz's inequality, and to investigate the equality and the bound of the inequality. As a consequence of this we present a Bernstein type inequality for nonselfadjoint operators. The Heinz inequality can be naturally extended to a more general case, and from which we obtain in particular Bessel's equality and inequality. Finally, Bernstein's inequality is extended to $n$ eigenvectors, and shows that the bound of the inequality is preserved.


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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/S0002-9939-97-03811-2
PII: S 0002-9939(97)03811-2
Received by editor(s): September 7, 1995
Received by editor(s) in revised form: September 19, 1995, and February 5, 1996
Dedicated: Dedicated to Professor Tien-Hoh Lin on his seventieth birthday and his retirement
Communicated by: Palle E. T. Jorgensen
Article copyright: © Copyright 1997 American Mathematical Society