International Journal of Mathematics and Mathematical Sciences
Volume 29 (2002), Issue 6, Pages 355-359
doi:10.1155/S016117120200652X
Multipliers on L(S), L(S)**, and LUC(S)* for a locally compact topological semigroup
Department of Mathematics, Teacher Training University, 566 Taleghani Avenue, Tehran 13614, Iran
Received 16 January 2001
Copyright © 2002 Alireza Medghalchi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Abstract
We study compact and weakly compact multipliers on
L(S), L(S)**, and LUC(S)*, where the latter is the dual of LUC(S). We show that a left cancellative semigroup S is left amenable if and only if there is a nonzero compact (or weakly compact) multiplier on L(S)**. We also prove that S is left amenable if and only if there is a nonzero compact (or weakly compact) multiplier on LUC(S)*.