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Heinz's inequality and Bernstein's inequality

Author(s): C.-S. Lin
Journal: Proc. Amer. Math. Soc. 125 (1997), 2319-2325.
MSC (1991): Primary 47A30, 65F15; Secondary 65J10
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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.

References:

1.: H. J. Bernstein, An inequality for selfadjoint operators in a Hilbert space, Proc. Amer. Math. Soc., 100 (1987), 319-321. MR 89b:47013a
2.: T. Furuta, Two mixed Hadamard type generalizations of Heinz inequality, Proc. Amer. Math. Soc., 103 (1988), 91-96. MR 89e:47009
3.: E. Heinz, On an inequality for linear operators in a Hilbert space. Report on Operator Theory and Group Representations, No. 387, National Academy of Science, USA, 1995, 27-29. MR 18:35b
4.: W. Rudin, Functional Analysis, McGraw-Hill Book Company, 1973. MR 51:1315

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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: 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
Copyright of article: Copyright 1997, American Mathematical Society

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C.-S. Lin, Heinz's inequality and Bernstein's inequality, Proceedings of the American Mathematical Society, 8, vol. 125, Proceedings of the American Mathematical Society, 1997, pp. 2319-2325.


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