Abstract.
We study representations of numerical semigroups ∑ by isometries on Hilbert space with commuting range projections. Our main theorem says that each such representation is unitarily equivalent to the direct sum of a representation by unitaries and a finite number of multiples of particular concrete representations by isometries. We use our main theorem to identify the faithful representations of the C*-algebra C*(∑) generated by a universal isometric representation with commuting range projections, and also prove a structure theorem for C*(∑).
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This research was supported by the Australian Research Council.
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Vittadello, S.T. The Isometric Representation Theory of Numerical Semigroups. Integr. equ. oper. theory 64, 573–597 (2009). https://doi.org/10.1007/s00020-009-1701-2
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DOI: https://doi.org/10.1007/s00020-009-1701-2