A class of weighted convolution Fréchet algebras

Thomas Vils Pedersen. "A class of weighted convolution Fréchet algebras." Banach Center Publications 91.1 (2010): 247-259. <http://eudml.org/doc/282055>.

@article{ThomasVilsPedersen2010,
abstract = {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.},
author = {Thomas Vils Pedersen},
journal = {Banach Center Publications},
keywords = {Fréchet algebra; endomorphism; continuous derivations},
language = {eng},
number = {1},
pages = {247-259},
title = {A class of weighted convolution Fréchet algebras},
url = {http://eudml.org/doc/282055},
volume = {91},
year = {2010},
}

TY - JOUR
AU - Thomas Vils Pedersen
TI - A class of weighted convolution Fréchet algebras
JO - Banach Center Publications
PY - 2010
VL - 91
IS - 1
SP - 247
EP - 259
AB - 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.
LA - eng
KW - Fréchet algebra; endomorphism; continuous derivations
UR - http://eudml.org/doc/282055
ER -