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 ...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 topology展开更多
文摘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 topology
