Heinz’s inequality and Bernstein’s inequality
HTML articles powered by AMS MathViewer
- by C.-S. Lin PDF
- Proc. Amer. Math. Soc. 125 (1997), 2319-2325 Request permission
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
- Herbert J. Bernstein, An inequality for selfadjoint operators on a Hilbert space, Proc. Amer. Math. Soc. 100 (1987), no. 2, 319–321. MR 884472, DOI 10.1090/S0002-9939-1987-0884472-8
- Takayuki Furuta, Two mixed Hadamard type generalizations of Heinz inequality, Proc. Amer. Math. Soc. 103 (1988), no. 1, 91–96. MR 938650, DOI 10.1090/S0002-9939-1988-0938650-0
- Cahit Arf, Untersuchungen über reinverzweigte Erweiterungen diskret bewerteter perfekter Körper, J. Reine Angew. Math. 181 (1939), 1–44 (German). MR 18, DOI 10.1515/crll.1940.181.1
- Walter Rudin, Functional analysis, McGraw-Hill Series in Higher Mathematics, McGraw-Hill Book Co., New York-Düsseldorf-Johannesburg, 1973. MR 0365062
Additional Information
- C.-S. Lin
- Affiliation: Department of Mathematics, Bishop’s University, Lennoxville, Quebec, Canada J1M 1Z7
- Email: plin@ubishops.ca
- Received by editor(s): September 7, 1995
- Received by editor(s) in revised form: September 19, 1995, and February 5, 1996
- Communicated by: Palle E. T. Jorgensen
- © Copyright 1997 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 125 (1997), 2319-2325
- MSC (1991): Primary 47A30, 65F15; Secondary 65J10
- DOI: https://doi.org/10.1090/S0002-9939-97-03811-2
- MathSciNet review: 1376997
Dedicated: Dedicated to Professor Tien-Hoh Lin on his seventieth birthday and his retirement