A Dilation and Norm in Several Variable Operator Theory

Binding, Paul ; Farenick, D. R. ; Li, Chi-Kwong

Canadian journal of mathematics, Tome 47 (1995) no. 3, pp. 449-461

Résumé

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.

Détail

DOI : 10.4153/CJM-1995-025-5

Mots-clés : 15A60, 47A20, 47A30

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