A class of weighted convolution Fréchet algebras
نویسنده
چکیده
For an increasing sequence (ωn) of algebra weights on R + we study various properties of the Fréchet algebra A(ω) = ⋂ n L (ωn) obtained as the intersection of the weighted Banach algebras L(ωn). We show that every endomorphism of A(ω) is standard, if for all n ∈ N there exists m ∈ N such that ωm(t)/ωn(t) → ∞ as t → ∞. Moreover, we characterise the continuous derivations on this algebra: If for all n ∈ N there exists m ∈ N such that t∗ωn(t)/ωm(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 is a measure in B(ω) = ⋂ n M(ωn) 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.
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