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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc91-0-10,
author = {Sandy Grabiner},
title = {Good weights for weighted convolution algebras},
journal = {Banach Center Publications},
volume = {89},
year = {2010},
pages = {179-189},
zbl = {1223.43003},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc91-0-10}
}
Sandy Grabiner. Good weights for weighted convolution algebras. Banach Center Publications, Tome 89 (2010) pp. 179-189. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc91-0-10/