For all convolution algebras L 1[0, 1); L loc1 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.
@article{bwmeta1.element.doi-10_2478_s11533-013-0373-y,
author = {Thomas Pedersen},
title = {Properties of derivations on some convolution algebras},
journal = {Open Mathematics},
volume = {12},
year = {2014},
pages = {742-751},
zbl = {1304.46043},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.doi-10_2478_s11533-013-0373-y}
}
Thomas Pedersen. Properties of derivations on some convolution algebras. Open Mathematics, Tome 12 (2014) pp. 742-751. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-013-0373-y/
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