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• W2003990468 abstract "Let A be a dense Fréchet *-subalgebra of a C*-algebra B. (We do not require Fréchet algebras to be m-convex.) Let G be a Lie group, not necessarily connected, which acts on both A and B by *-automorphisms, and let σ be a sub-polynomial function from G to the nonnegative real numbers. If σ and the action of G on A satisfy certain simple properties, we define a dense Fréchet *-subalgebra G ⋊ σ A of the crossed product L 1 (G, B). Our algebra consists of differentiable A-valued functions on G, rapidly vanishing in σ. We give conditions on σ and the action of G on A which imply the m-convexity of the dense subalgebra G ⋊ σ A. A locally convex algebra is said to be m-convex if there is a family of submultiplicative seminorms for the topology of the algebra. The property of m-convexity is important for a Fréchet algebra, and is useful in modern operator theory. If G acts as a transformation group on a locally compact space M, we develop a class of dense subalgebras for the crossed product L 1 (G, C 0 (M)), where C 0 (M) denotes the continuous functions on M vanishing at infinity with the sup norm topology. We define Schwartz functions S (M) on M, which are differentiable with respect to some group action on M, and are rapidly vanishing with respect to some scale on M. We then form a dense Fréchet *-subalgebra G ⋊ σ S (M) of rapidly vanishing, G-differentiable functions from G to S (M). If the reciprocal of σ is in L p (G) for some p, we prove that our group algebras S σ (G) are nuclear Fréchet spaces, and that G ⋊ σ A is the projective completion [Formula: see text]." @default.
• W2003990468 created "2016-06-24" @default.
• W2003990468 creator A5070925772 @default.
• W2003990468 date "1993-08-01" @default.
• W2003990468 modified "2023-09-23" @default.
• W2003990468 title "DENSE m-CONVEX FRÉCHET SUBALGEBRAS OF OPERATOR ALGEBRA CROSSED PRODUCTS BY LIE GROUPS" @default.
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• W2003990468 doi "https://doi.org/10.1142/s0129167x93000315" @default.
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