Similarity degree of Fourier algebras
Copyright policy )Similarity degree of Fourier algebras
We show that for a locally compact group $G$, amongst a class which contains amenable and small invariant neighbourhood groups, that its Fourier algebra $A(G)$ satisfies a completely bounded version Pisier's similarity property with similarity degree at most $2$. Specifically, any completely bounded homomorphism $��: A(G)\to B(H)$ admits an invertible $S$ in $B(H)$ for which $\|S\|\|S^{-1}\|\leq ||��||_{cb}^2$ and $S^{-1}��(\cdot)S$ extends to a $*$-representation of the $C^*$-algebra $C_0(G)$. This significantly improves some results due to Brannan and Samei (J. Funct. Anal. 259, 2010) and Brannan, Daws and Samei (M��nster J. Math 6, 2013). We also note that $A(G)$ has completely bounded similarity degree $1$ if and only if it is completely isomorphic to an operator algebra if and only if $G$ is finite.
14 pages; Final version to appear in JFA
- Seoul National University Korea (Republic of)
- University of Saskatchewan Canada
- University of Waterloo Canada
small invariant neighbourhood, representation, Means on groups, semigroups, etc.; amenable groups, Mathematics - Operator Algebras, completely bounded map, Functional Analysis (math.FA), Fourier algebra, Mathematics - Functional Analysis, operator space, amenable groups, Representations of topological algebras with involution, FOS: Mathematics, Operator spaces and completely bounded maps, Fourier and Fourier-Stieltjes transforms on nonabelian groups and on semigroups, etc., Operator Algebras (math.OA), similarity degree, Primary 46K10, Secondary 43A30, 46L07, 43A07
small invariant neighbourhood, representation, Means on groups, semigroups, etc.; amenable groups, Mathematics - Operator Algebras, completely bounded map, Functional Analysis (math.FA), Fourier algebra, Mathematics - Functional Analysis, operator space, amenable groups, Representations of topological algebras with involution, FOS: Mathematics, Operator spaces and completely bounded maps, Fourier and Fourier-Stieltjes transforms on nonabelian groups and on semigroups, etc., Operator Algebras (math.OA), similarity degree, Primary 46K10, Secondary 43A30, 46L07, 43A07
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).7 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Top 10% impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!