Abstract
An infinite direct product ⊗ ∞ i =1 U i (a) of continuous unitary representations of SL(2,C) in Hilbert spaces ℌ i is continuous only on certain incomplete direct product subspaces of ⊗ ∞ i =1 ℌ i . If no representations of the complementary series occur, then each of these subspaces contains a product vector almost all factors of which are SL(2, C)-invariant.
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Polley, L. On infinite direct products of Lorentz transformations. Lett Math Phys 4, 227–233 (1980). https://doi.org/10.1007/BF00316678
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DOI: https://doi.org/10.1007/BF00316678