Hostname: page-component-78c5997874-ndw9j Total loading time: 0 Render date: 2024-11-19T14:42:37.622Z Has data issue: false hasContentIssue false
  • English
  • Français

Unitary dilations, polynomial identities and the von Neumann inequality

Published online by Cambridge University Press:  24 October 2008

P. G. Dixon  and
S. W. Drury
P. G. Dixon
Affiliation:
Department of Pure Mathematics, University of Sheffield, Sheffield S3 7RH
S. W. Drury
Affiliation:
Department of Mathematics, McGill University, Montreal H3A 2K6, Canada
Get access Rights & Permissions [Opens in a new window]

Extract

Let p(X1, …, Xn) be a polynomial in the commuting indeterminates X1, …, Xn.

Define

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 99 , Issue 1 , January 1986 , pp. 115 - 122
Copyright
Copyright © Cambridge Philosophical Society 1986

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

REFERENCES

[1]Ando, T.. On a pair of commutative contractions. Acta Sci. Math. 24 (1963), 88–90.Google Scholar
[2]Cohn, P. M.. Algebra, vol. 2 (Wiley, 1977).Google Scholar
[3]Crabb, M. J. and Davie, A. M.. von Neumann's inequality for Hilbert space operators. Bull. London Math. Soc. 7 (1975), 49–50.Google Scholar
[4]Dixon, P. G.. The von Neumann inequality for polynomials of degree greater than two. J. London Math. Soc. (2) 14 (1976), 369–375.Google Scholar
[5]Drury, S. W.. Remarks on von Neumann's inequality. In Banach Spaces, Harmonic Analysis and Probability Theory, Lecture Notes in Math. 995 (Springer-Verlag, 1983), pp. 14–32.CrossRefGoogle Scholar
[6]Formanek, E.. The polynomial identities of matrices. In Algebraists' Homage: Papers in Ring Theory and Related Topics, Contemporary Mathematics, vol. 13 (Amer. Math. Soc, 1982).Google Scholar
[7]Parrott, S.. Unitary dilations for commuting contractions. Pacific J. Math. 34 (1970), 481–490.Google Scholar
[8]Rowen, L. H.. Polynomial Identities in Ring Theory (Academic Press, 1980).Google Scholar
[9]Nagy, B. Sz.. Unitary Dilations of Hilbert Space Operators and Related Topics, C.B.M.S.Regional Conference Series in Mathematics 19 (Amer. Math. Soc, 1974).Google Scholar
[10]Nagy, B. Sz. and Foiaş, C.. Harmonic Analysis of Operators on Hilbert Space (North-Holland, 1970).Google Scholar
[11]Tonge, A.. The von Neumann inequality for polynomials in several Hilbert-Schmidt operators. J. London Math. Soc. (2) 18 (1978), 519–526.Google Scholar
[12]Varopoulos, N. Th.. On an inequality of von Neumann and an application of the metric theory of tensor products to operator theory. J. Functional Analysis, 16 (1974), 83–100.CrossRefGoogle Scholar
[13]Varopoulos, N. Th.. On a commuting family of contractions on a Hilbert space. Rev. Roum. Math. Pures et Appl. 21 (1976), 1283–1285.Google Scholar
[14]von Neumann, J.. Eine Spectraltheorie für allgemeine Operatoren eines unitären Raumes. Math. Nachr. 4 (1951), 258–281.Google Scholar