Abstract
Let G be a locally compact group, always assumed Hausdorff. Let H be a Banach space (which in most of our applications will be a Hubert space). A representation of G in H is a homomorphism
of G into the group of continuous linear automorphisms of H, such that for each vector v ∈ H the map of G into H given by
is continuous. One may say that the homomorphism is strongly continuous, the strong topology being the norm topology on the Banach space. [We recall here that the weak topology on H is that topology having the smallest family of open sets for which all functionals on H are continuous.]
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© 1985 Springer-Verlag New York Inc.
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Lang, S. (1985). General Results. In: SL 2(R). Graduate Texts in Mathematics, vol 105. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-5142-2_1
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DOI: https://doi.org/10.1007/978-1-4612-5142-2_1
Publisher Name: Springer, New York, NY
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