A Dilation and Norm in Several Variable Operator Theory

Abstract

AbstractFor 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.