A class of weighted convolution Fréchet algebras

• Autorzy: Thomas Vils Pedersen
• Języki publikacji: EN

Abstrakty

EN

For an increasing sequence (ωₙ) of algebra weights on ℝ⁺ we study various properties of the Fréchet algebra A(ω) = ⋂ ₙ L¹(ωₙ) obtained as the intersection of the weighted Banach algebras L¹(ωₙ). We show that every endomorphism of A(ω) is standard, if for all n ∈ ℕ there exists m ∈ ℕ such that $ω_m(t)/ωₙ(t) → ∞$ as t → ∞. Moreover, we characterise the continuous derivations on this algebra: Let M(ωₙ) be the corresponding weighted measure algebras and let B(ω) = ⋂ ₙM(ωₙ). If for all n ∈ ℕ there exists m ∈ ℕ such that $tωₙ(t)/ω_m(t)$ is bounded on ℝ⁺, then the continuous derivations on A(ω) are exactly the linear maps D of the form D(f) = (Xf)*μ for f ∈ A(ω), where μ ∈ B(ω) and (Xf)(t) = tf(t) for t ∈ ℝ⁺ and f ∈ A(ω). If the condition is not satisfied, we show that A(ω) has no non-zero derivations.

Kategorie tematyczne

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

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2010
• Tom: 91
• Numer: 1
• Strony: 247-259

Daty

wydano

2010

Twórcy

autor

Thomas Vils Pedersen

• Department of Basic Sciences and Environment, University of Copenhagen, Thorvaldsensvej 40, DK-1871 Frederiksberg C, Denmark

Identyfikatory

DOI

10.4064/bc91-0-15