Separating maps on weighted function algebras on topological groups |
| |
| Authors: | Saeid Maghsoudi Rasoul Nasr-Isfahani |
| |
| Institution: | (1) Central Research Laboratory (Nakahari Project), Osaka Medical College, 2-7 Daigakucho, Takatsuki 569-8686, Japan;(2) Department of Physiology, Osaka Medical College, 2-7 Daigakucho, Takatsuki 569-8686, Japan;(3) Department of Chemistry, Osaka Medical College, 2-7 Daigakucho, Takatsuki 569-8686, Japan;(4) Department of Internal Medicine, Osaka Medical College, 2-7 Daigakucho, Takatsuki 569-8686, Japan;(5) Department of Molecular Cell Physiology, Graduate School of Medical Science, Kyoto Prefectural University of Medicine, Kyoto, Japan;(6) Department of Pediatrics, Graduate School of Medical Science, Kyoto Prefectural University of Medicine, Kyoto, Japan |
| |
| Abstract: | Let G
1 and G
2 be locally compact groups and let ω
1 and ω
2 be weight functions on G
1 and G
2, respectively. For i = 1, 2, let also C
0(G
i
, 1/ω
i
) be the algebra of all continuous complex-valued functions f on G
i
such that f/ω
i
vanish at infinity, and let H: C
0(G
1, 1/ω
1) → C
0(G
2, 1/ω
2) be a separating map; that is, a linear map such that H(f)H(g) = 0 for all f, g ∈ C
0(G
1, 1/ω
1) 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 ℴ h) for all f ∈ C
0(G
1, 1/ω
1), where φ: G
2 → ℂ is a non-vanishing continuous function and h: G
2 → G
1 is a topological isomorphism. Finally, we offer a statement equivalent to that h is also a group homomorphism. |
| |
| Keywords: | |
| 本文献已被 SpringerLink 等数据库收录！ |
|
