Properties of derivations on some convolution algebras

Original · EN

For all the convolution algebras L¹[0,1),L¹loc and A(ω)=ₙ L¹(ωₙ), the derivations are of the form Dμ f=Xf*μ for suitable measures μ, where (Xf)(t)=tf(t). We describe the (weakly) compact as well as the (weakly) Montel derivations on these algebras in terms of properties of the measure μ. Moreover, for all these algebras we show that the extension of Dμ to a natural dual space is weak-star continuous.