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- W2050606119 abstract "Let G be a finite-dimensional Lie group, and let E be a locally convex topological G-module. If E is sequentially complete, then E and the space E∞ of smooth vectors are Cc∞(G)-modules, but the module multiplication need not be continuous. The pathology can be ruled out if E is (or embeds into) a projective limit of Banach G-modules. Moreover, in this case Eω (the space of analytic vectors) is a module for the algebra A(G) of superdecaying analytic functions introduced by Gimperlein, Krötz, and Schlichtkrull. We prove that Eω is a topological A(G)-module if E is a Banach space or, more generally, if every countable set of continuous seminorms on E has an upper bound. The same conclusion is obtained if G has a compact Lie algebra. The question of whether Cc∞(G) and A(G) are topological algebras is also addressed." @default.
- W2050606119 created "2016-06-24" @default.
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- W2050606119 date "2013-01-01" @default.
- W2050606119 modified "2023-10-14" @default.
- W2050606119 title "Continuity of LF-algebra representations associated to representations of Lie groups" @default.
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- W2050606119 doi "https://doi.org/10.1215/21562261-2265895" @default.
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