IJPAM: Volume 16, No. 1 (2004)

2-WEAK AMENABILITY OF A BEURLING
ALGEBRA AND AMENABILITY OF ITS SECOND DUAL

F. Ghahramani$^1$, G. Zabandan$^2$
$^1$Department of Mathematics
University of Manitoba
Winnipeg, Manitoba, R3T 2N2, CANADA
e-mail: fereidou@cc.umanitoba.ca
$^2$Teacher Training University
49 Mofateh Av., Tehran, IRAN
e-mail: zabandan@saba.tmu.ac.ir


Abstract.We show that the second dual algebra of a Beurling algebra on a locally compact group $G$ is amenable if and only if $G$ is finite. We also show that if $G$ is Abelian, then the Beurling algebra $L^1(G,w)$ is 2-weakly amenable if for every $t \in G$, ${\inf_n} {w (nt) \over n} = 0$ and the function $\Omega(x) = {\lim \sup}_{t \to \infty} {w (x + t) \over w(t)}$, $(x \in G)$, is bounded.

Received: July 6, 2004

AMS Subject Classification: 43A20, 46H20

Key Words and Phrases: amenability, Beurling algebra, derivation

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2004
Volume: 16
Issue: 1