Properties of derivations on some convolution algebras

Thomas Pedersen

Open Mathematics (2014)

  • Volume: 12, Issue: 5, page 742-751
  • ISSN: 2391-5455

Abstract

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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.

How to cite

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Thomas Pedersen. "Properties of derivations on some convolution algebras." Open Mathematics 12.5 (2014): 742-751. <http://eudml.org/doc/269502>.

@article{ThomasPedersen2014,
abstract = {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.},
author = {Thomas Pedersen},
journal = {Open Mathematics},
keywords = {Convolution algebras; Derivations; Compactness; Weak-star continuity; convolution algebras; derivations; compactness; weak* continuity},
language = {eng},
number = {5},
pages = {742-751},
title = {Properties of derivations on some convolution algebras},
url = {http://eudml.org/doc/269502},
volume = {12},
year = {2014},
}

TY - JOUR
AU - Thomas Pedersen
TI - Properties of derivations on some convolution algebras
JO - Open Mathematics
PY - 2014
VL - 12
IS - 5
SP - 742
EP - 751
AB - 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.
LA - eng
KW - Convolution algebras; Derivations; Compactness; Weak-star continuity; convolution algebras; derivations; compactness; weak* continuity
UR - http://eudml.org/doc/269502
ER -

References

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  13. [13] Pedersen T.V., Compactness and weak-star continuity of derivations on weighted convolution algebras, J. Math. Anal. Appl., 2013, 397(1), 402–414 http://dx.doi.org/10.1016/j.jmaa.2012.07.057 Zbl1256.43001
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