suppose $pi:mathcal{a}rightarrow mathcal{b}$ is a surjective unital $ast$-homomorphism between c*-algebras $mathcal{a}$ and $mathcal{b}$, and $0leq aleq1$ with $ain  mathcal{a}$. we give a sufficient condition that ensures there is a proection $pin mathcal{a}$ such that $pi left( pright) =pi left( aright) $. an easy consequence is a result of [l. g. brown and g. k. pedersen, c*-algebras of real...

let g be a locally compact group, and let ω be a weight on g. we show that the weightedmeasure algebra m(g,ω) is amenable if and only if g is a discrete, amenable group andsup{ω(g) ω(g−1) : g ∈ g} < ∞, where ω(g) ≥ 1 (g ∈ g) .

the weighted semigroup algebra mb (s, w) is studied via its identification with mb (s) together with a weighted algebra product *w so that (mb (s, w), *) is isometrically isomorphic to (mb (s), *w). this identification enables us to study the relation between regularity and amenability of mb (s, w) and mb (s), and improve some old results from discrete to general case.