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Representation theory of \(U_ 1(H)\) in the symmetric tensors. (English) Zbl 0675.46025

Summary: The representations of the group of unitary operators which are trace- class perturbations of the identity on an infinite-dimensional separable Hilbert space are classified according to factoriality, quasi- equivalence, and semifiniteness, by relating these representations to the quasi-free representations of the Weyl algebra. This answers the problem posed by Ş. Strǎtilǎ and D. Voiculescu [Representation of AF-algebras and of the group U(\(\infty)\), Lect. Notes Math. 486 (1975; Zbl 0318.46069)].

MSC:

46L05 General theory of \(C^*\)-algebras
47D03 Groups and semigroups of linear operators

Citations:

Zbl 0318.46069
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References:

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