We consider weighted semigroup algebra $M_b(S,w)$ as the Banach

algebra $M_b(S)$ together a weighted algebra product $*_w$ so that

$(M_b(S,w), *)$ is algebra-isomorphic and isometric with

$(M_b(S),*_w)$. ...

other things, that the topological (algebraic) center of the Banach algebra UCl(K)* is M(K), the measure algebra of K....