# A class of weighted convolution Fréchet algebras

Banach Center Publications (2010)

- Volume: 91, Issue: 1, page 247-259
- ISSN: 0137-6934

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topThomas 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 -

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