Journal Article10.4153/CJM-1995-025-5
A Dilation and Norm in Several Variable Operator Theory
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TL;DR: In this article, a norm on the m-fold cartesian product of ℬ(ℋ) 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.
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Abstract: 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.
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References
•Book
Banach Algebra Techniques in Operator Theory
Ronald G. Douglas
- 11 Feb 1972
TL;DR: In this paper, the authors propose a compact operator on Hilbert Space and C*-Algebras, as well as Compact Operators, Fredholm Operators and Index Theory.
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