312 research outputs found
Finite dimensional irreducible representations and the uniqueness of the Lebesgue decomposition of positive functionals
We prove for an arbitrary complex -algebra that every topologically
irreducible -representation of on a Hilbert space is finite dimensional
precisely when the Lebesgue decomposition of representable positive functionals
over is unique. In particular, the uniqueness of the Lebesgue decomposition
of positive functionals over the -algebras of locally compact groups
provides a new characterization of Moore groups.Comment: To appear in: Journal of Operator Theor
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