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Weak* properties of weighted convolution algebras II

100%
Grabiner S.
Studia Mathematica
|
2010
|
tom 198
|
nr 1
53-67
EN
We show that if ϕ is a continuous homomorphism between weighted convolution algebras on ℝ⁺, then its extension to the corresponding measure algebras is always weak* continuous. A key step in the proof is showing that our earlier result that normalized powers of functions in a convolution algebra on ℝ⁺ go to zero weak* is also true for most measures in the corresponding measure algebra. For some algebras, we can determine precisely which measures have normalized powers converging to zero weak*. We also include a variety of applications of weak* results, mostly to norm results on ideals and on convergence.
2
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Good weights for weighted convolution algebras

100%
Grabiner S.
Banach Center Publications
|
2010
|
tom 91
|
nr 1
179-189
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.
3
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Weighted convolution algebras and their homomorphisms

100%
Grabiner S.
Banach Center Publications
|
1994
|
tom 30
|
nr 1
175-190
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