Properties of derivations on some convolution algebras

TY - JOUR

T1 - Properties of derivations on some convolution algebras

AU - Pedersen, Thomas Vils

PY - 2014/5

Y1 - 2014/5

N2 - For all convolution algebras L 1[0, 1); L loc 1 and A(ω) = ∩n L 1(ωn), the derivations are of the form D μ 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 D μ to a natural dual space is weak-star continuous.

AB - For all convolution algebras L 1[0, 1); L loc 1 and A(ω) = ∩n L 1(ωn), the derivations are of the form D μ 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 D μ to a natural dual space is weak-star continuous.

U2 - 10.2478/s11533-013-0373-y

DO - 10.2478/s11533-013-0373-y

M3 - Journal article

SN - 1895-1074

VL - 12

SP - 742

EP - 751

JO - Central European Journal of Mathematics

JF - Central European Journal of Mathematics

IS - 5

ER -