English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Tools annual

Global: Zendy Free Plan

Global: Zendy Tools monthly

Global: Zendy Plus monthly

Let A be a dense Frechet *-subalgebra of a C*-algebra B. (We do not requireFrechet algebras to be m-convex.) Let G be a Lie group, not necessarily con-nected, which acts on both $A$ and B by *-automorphisms, and let \s be a sub-multiplicative function from G to the nonnegative real numbers. If \s and theaction of G on A satisfy certain simple properties, we define a dense Frechet*-subalgebra G\rtimes^{\s} A of the crossed product L^{1}(G, B). Our algebraconsists of differentiable A-valued functions on G, rapidly vanishing in \s.  We give conditions on the action of G on A which imply the m-convexity of thedense subalgebra G\rtimes^{\s}A. A locally convex algebra is said to be m-con-vex if there is a family of submultiplicative seminorms for the topology of thealgebra. The property of m-convexity is important for a Frechet algebra, and isuseful in modern operator theory.  If G acts as a transformation group on a manifold M, we develop a class ofdense 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 normtopology.We define Schwartz functions S(M) on M, which are differentiable withrespect to some group action on M, and are rapidly vanishing with respect tosome scale on M. We then form a dense m-convex Frechet *-subalgebra G\rtimes^{\s} S(M) of rapidly vanishing, G-differentiable functions from G to S(M).  If the reciprocal of \s is in L^{p}(G) for some p, we prove that our groupalgebras S^{\s}(G) are nuclear Frechet spaces, and that G\rtimes^{\s}A is theprojective completion S^{\s}(G) \otimes A.

DENSE m-CONVEX FRÉCHET SUBALGEBRAS OF OPERATOR ALGEBRA CROSSED PRODUCTS BY LIE GROUPS