Abstract
We discuss the infinite product of unitary operators in an incomplete direct product of Hilbert spaces. Necessary and sufficient conditions are derived under which this infinite product leads to a continuous unitary one-parameter group provided each factor is assumed to have this property. A certain minimal condition guarantees the existence of a renormalized unitary group. An application is made to product representations of the canonical commutation relations in order to determine the admissible test functions.
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Communicated by H. Araki
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Reents, G. On infinite direct products of continuous unitary one-parameter groups. Commun.Math. Phys. 39, 121–130 (1974). https://doi.org/10.1007/BF01608391
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DOI: https://doi.org/10.1007/BF01608391