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Separating maps on weighted function algebras on topological groups

In: Mathematica Slovaca, vol. 61, no. 6
Saeid Maghsoudi - Rasoul Nasr-Isfahani

Details:

Year, pages: 2011, 941 - 948
Keywords:
convolution quasi-homomorphism, locally compact group, separating map, weight function, weighted function algebras
About article:
Let $G1$ and $G2$ be locally compact groups and let $ω1$ and $ω2$ be weight functions on $G1$ and $G2$, respectively. For $i=1,2$, let also $C0(Gi,1/ωi)$ be the algebra of all continuous complex-valued functions $f$ on $Gi$ such that $f/ωi$ vanish at infinity, and let $H:C0(G1,1/ω1)\rightarrow C0(G2,1/ω2)$ be a separating map; that is, a linear map such that $H(f)H(g)=0$ for all $f,g\in C0(G1,1/ω1)$ with $fg=0$. In this paper, we study conditions under which $H$ can be represented as a weighted composition map; i.e.,$H(f)=φ(f\circ h)$ for all $f\in C0(G1,1/ω1)$, where$φ:G2\rightarrow \Bbb C$ is a non-vanishing continuous function and $h:G2 \rightarrow G1$ is a topological isomorphism. Finally, we offer a statement equivalent to that $h$ is also a group homomorphism.
How to cite:
ISO 690:
Maghsoudi, S., Nasr-Isfahani, R. 2011. Separating maps on weighted function algebras on topological groups. In Mathematica Slovaca, vol. 61, no.6, pp. 941-948. 0139-9918. DOI: https://doi.org/10.2478/s12175-011-0060-z

APA:
Maghsoudi, S., Nasr-Isfahani, R. (2011). Separating maps on weighted function algebras on topological groups. Mathematica Slovaca, 61(6), 941-948. 0139-9918. DOI: https://doi.org/10.2478/s12175-011-0060-z
About edition: