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Weak-1 generators for a class of subalgebras of l1
Authors:Raymond C Roan
Institution:University of Kentucky, Lexington, Kentucky 40506 USA
Abstract:Let α ? 0 and let D(α) = {f(z) = ∑0αnzn ¦ ∑0 (n + 1)α¦ an ¦ < ∞}. Then D(α) is a subalgebra of l1. We discuss the weak-1 generators of D(α). We use some of our techniques to prove that if ? is a weak-1 generator of H and ∥ ? ∥ ? 1, then the composition operator C? on the Dirichlet space has dense range.
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