# Good weights for weighted convolution algebras

• Volume: 91, Issue: 1, page 179-189
• ISSN: 0137-6934

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## Abstract

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Weighted convolution algebras L¹(ω) on R⁺ = [0,∞) have been studied for many years. At first results were proved for continuous weights; and then it was shown that all such results would also hold for properly normalized right continuous weights. For measurable weights, it was shown that one could construct a properly normalized right continuous weight ω' with L¹(ω') = L¹(ω) with an equivalent norm. Thus all algebraic and norm-topology results remained true for measurable weights. We now show that, with careful definitions, the same is true for the weak* topology on the space of measures that is the dual of the space of continuous functions C₀(1/ω). We give the new result and a survey of the older results, with several improved statements and/or proofs of theorems.

## How to cite

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Sandy Grabiner. "Good weights for weighted convolution algebras." Banach Center Publications 91.1 (2010): 179-189. <http://eudml.org/doc/281980>.

@article{SandyGrabiner2010,
abstract = {Weighted convolution algebras L¹(ω) on R⁺ = [0,∞) have been studied for many years. At first results were proved for continuous weights; and then it was shown that all such results would also hold for properly normalized right continuous weights. For measurable weights, it was shown that one could construct a properly normalized right continuous weight ω' with L¹(ω') = L¹(ω) with an equivalent norm. Thus all algebraic and norm-topology results remained true for measurable weights. We now show that, with careful definitions, the same is true for the weak* topology on the space of measures that is the dual of the space of continuous functions C₀(1/ω). We give the new result and a survey of the older results, with several improved statements and/or proofs of theorems.},
author = {Sandy Grabiner},
journal = {Banach Center Publications},
keywords = {convolution algebra; weight; equivalent weights},
language = {eng},
number = {1},
pages = {179-189},
title = {Good weights for weighted convolution algebras},
url = {http://eudml.org/doc/281980},
volume = {91},
year = {2010},
}

TY - JOUR
AU - Sandy Grabiner
TI - Good weights for weighted convolution algebras
JO - Banach Center Publications
PY - 2010
VL - 91
IS - 1
SP - 179
EP - 189
AB - Weighted convolution algebras L¹(ω) on R⁺ = [0,∞) have been studied for many years. At first results were proved for continuous weights; and then it was shown that all such results would also hold for properly normalized right continuous weights. For measurable weights, it was shown that one could construct a properly normalized right continuous weight ω' with L¹(ω') = L¹(ω) with an equivalent norm. Thus all algebraic and norm-topology results remained true for measurable weights. We now show that, with careful definitions, the same is true for the weak* topology on the space of measures that is the dual of the space of continuous functions C₀(1/ω). We give the new result and a survey of the older results, with several improved statements and/or proofs of theorems.
LA - eng
KW - convolution algebra; weight; equivalent weights
UR - http://eudml.org/doc/281980
ER -

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