Good weights for weighted convolution algebras

• Autorzy: Sandy Grabiner
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 43A20: L 1 -algebras on groups, semigroups, etc.
• 43A10: Measure algebras on groups, semigroups, etc.

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Banach Center Publications
• Rocznik: 2010
• Tom: 91
• Numer: 1
• Strony: 179-189

Daty

wydano

2010

Twórcy

autor

Sandy Grabiner

• Department of Mathematics, Pomona College, 610 N. College Avenue, Claremont, CA 91711, U.S.A.

Identyfikatory

DOI

10.4064/bc91-0-10