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Tensor products of subnormal operators

Authors:	Nathan S Feldman

Institution:	Department of Mathematics, Michigan State University, East Lansing, Michigan 48824-1027

Abstract:	We shall use a -algebra approach to study operators of the form $S \otimes N$ where is subnormal and is normal. We shall determine the spectral properties for these operators, and find the minimal normal extension and the dual operator. We also give a necessary condition for $C^(S \otimes N)$ to contain a compact operator and a sufficient condition for the algebraic equivalence of $S \otimes N$ and $S \otimes M$ . We also consider the existence of a homomorphism $\phi:C^(S \otimes T) \to C^*(S)$ satisfying $\phi(S \otimes T) = S$ . We shall characterize the operators such that $\phi$ exists for every operator . The problem of when $S \otimes N$ is unitarily equivalent to $S \otimes M$ is considered. Complete results are given when and are positive operators with finite multiplicity functions and has compact self-commutator. Some examples are also given.

Keywords:	Tensor product subnormal operator dual operator

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