Weak* Properties of Weighted Convolution Algebras
Suppose that L1(ω) is a weighted convolution algebra on R+ = [0,∞) with the weight ω(t) normalized so that the corresponding space M(ω) of measures is the dual space of the space C0(1/ω) of continuous functions. Suppose that φ : L1(ω) → L1(ω0 ) is a continuous nonzero homomorphism, where L1(ω0 ) is also a convolution algebra. If L1(ω)∗f is norm dense in L1(ω), we show that L1(ω0 ) ∗ φ(f) is (relatively) weak∗ dense in L1(ω0 ), and we identify the norm closure of L1(ω0 ) ∗ φ(f) with...[Show more]
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