Abstract
We prove analogs of the Kaplansky Density Theorem and the Kadison Transitivity Theorem for irreducible representations of a real C*-algebra on a real Hilbert space. Specifically, if a C*-algebra is acting irreducibly on a real Hilbert space, then the Hilbert space has either a real, complex, or quaternionic structure with respect to which the density and transitivity theorems hold.
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Boersema, J.L. Kaplansky Density and Kadison Transitivity Theorems for Irreducible Representations of Real C*-Algebras. Acta Math Sinica 23, 1827–1832 (2007). https://doi.org/10.1007/s10114-005-0825-9
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DOI: https://doi.org/10.1007/s10114-005-0825-9