Properties of derivations on some convolution algebras

Thomas Vils Pedersen

doi:10.2478/s11533-013-0373-y

Properties of derivations on some convolution algebras

Institut for Matematiske Fag

Abstract

For all convolution algebras L1[0; 1); L1 loc and A(!) = T n L1(!n), the derivations are of the form Dμf = 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.

Originalsprog	Engelsk
Tidsskrift	Central European Journal of Mathematics
Vol/bind	12
Udgave nummer	5
Sider (fra-til)	742-751
ISSN	1895-1074
DOI	https://doi.org/10.2478/s11533-013-0373-y
Status	Udgivet - maj 2014

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10.2478/s11533-013-0373-y

Citationsformater

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abstract = "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.",

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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 -

Properties of derivations on some convolution algebras

Abstract

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