Strict Topology over the Space of Measures with Continuous Translations on a Locally Compact Foundation Semigroup  

作　　者：S. MAGHSOUDI R. NASR-ISFAHANI 

机构地区：[1]Department of Mathematics, Faculty of Sciences, Zanjan University, Zanjan 313, Iran [2]Department of Mathematical Sciences, Isfahan University of Technology, Isfahan 84156-83111, Iran

出　　处：《Acta Mathematica Sinica,English Series》2011年第5期933-942,共10页数学学报（英文版）

摘　　要：Let δ be a locally compact semigroup, w be a weight function on δ, and Ma （δ, ω） be the weighted semigroup algebra of δ. Let L0^∞（δ; Ma（δ, ω）） be the C＊-algebra of all Ma（δ, w）-measurable functions g on δ such that g/w vanishes at infinity. We introduce and study a strict topologyβ1 （δ, ω） on Ma（δ, ω） and show that the Banach space L0^∞（6;Ma（δ, ω） can be identified with the dual of Ma（δ, ω） endowed with 31（δ, ω）. We finally investigate some properties of the locally convex topology β^1（δ, ω） on Mo（δ, ω）. Keywords Foundation semigroup, locally convex space, weighted semigroup algebra, strict topologyLet δ be a locally compact semigroup, w be a weight function on δ, and Ma （δ, ω） be the weighted semigroup algebra of δ. Let L0^∞（δ; Ma（δ, ω）） be the C＊-algebra of all Ma（δ, w）-measurable functions g on δ such that g/w vanishes at infinity. We introduce and study a strict topologyβ1 （δ, ω） on Ma（δ, ω） and show that the Banach space L0^∞（6;Ma（δ, ω） can be identified with the dual of Ma（δ, ω） endowed with 31（δ, ω）. We finally investigate some properties of the locally convex topology β^1（δ, ω） on Mo（δ, ω）. Keywords Foundation semigroup, locally convex space, weighted semigroup algebra, strict topology

关 键 词：Foundation semigroup locally convex space weighted semigroup algebra strict topology 

分 类 号：O177.2[理学—数学] O211.4[理学—基础数学]