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A Dilation and Norm in Several Variable Operator Theory

Published online by Cambridge University Press:  20 November 2018

Paul Binding ,
D. R. Farenick  and
Chi-Kwong Li
Paul Binding
Affiliation:
Department of Mathematics and Statistics, University of Calgary, Calgary, Alberta, T2N1N4
D. R. Farenick
Affiliation:
Department of Mathematics and Statistics, University of Regina, Regina, Saskatchewan, S4S 0A2
Chi-Kwong Li
Affiliation:
Department of Mathematics, College of William and Mary, Williamsburg, Virginia 23187-8795, U.S.A.
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Abstract

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For every m-tuple of operators acting on a Hilbert space, it is shown that there exists a common dilation of these operators to mcommuting normal operators on some larger Hilbert space. We then introduce a norm on the m-fold cartesian product of ℬ(ℋ) that is defined to be, for a given w-tuple, the infimum of the joint spectral radii of all joint normal dilations of the m operators. This norm has several good features, one of which is that it is invariant under the passage to adjoints.

Keywords

15A6047A2047A30
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 47 , Issue 3 , 01 June 1995 , pp. 449 - 461
Copyright
Copyright © Canadian Mathematical Society 1995

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