Abstract

If A is an irreducible essentially normal operator, then we prove that the C^*-algebra generated by A has a finite number of irreducible subnormal operators as generators if and only if the essential spectrum of A is uncountable. It is shown that, in general, at most eight irreducible subnormal generators are required. Additionally, it is shown that frequently two irreducible subnormal operators will suffice and that, in many instances, the subnormal operators can be taken to be unilateral shifts of multiplicity one or unitarily equivalent to the dual of the Bergman shift.

Paper

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