Properties of derivations on some convolution algebras

• Autorzy: Thomas Pedersen
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

Convolution algebras; Derivations; Compactness; Weak-star continuity

Kategorie tematyczne

• 46H99: None of the above, but in this section
• 46E30: Spaces of measurable functions ( L p -spaces, Orlicz spaces, K\"othe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
• 47B07: Operators defined by compactness properties
• 46J99: None of the above, but in this section
• 47B47: Commutators, derivations, elementary operators, etc.

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2014
• Tom: 12
• Numer: 5
• Strony: 742-751

Daty

wydano

2014-05-01

online

2014-02-15

Twórcy

autor

Thomas Pedersen

• University of Copenhagen

Bibliografia

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Identyfikatory

DOI

10.2478/s11533-013-0373-y