Good weights for weighted convolution algebras
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.