Vol. 105, No. 1, 1983

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Closed ideals of l1(ωn) when {ωn} is star-shaped

Mark Phillip Thomas

Vol. 105 (1983), No. 1, 237–255

Let A = l1(ωn) be a radical Banach algebra of power series where the weight {ωn} is star-shaped. Let T be the operator of right translation on A. We give sufficient conditions for all closed ideals of A to be standard. These cases are more general than those previously considered, since in all these cases, T is unicellular but not a basis operator. We also construct a large class of such algebras A in which there are elements x such that the closed ideal (Ax) is standard, but the algebraic ideal Ax contains no power of z.

Mathematical Subject Classification 2000
Primary: 46J05
Secondary: 47D30
Received: 29 April 1981
Published: 1 March 1983
Mark Phillip Thomas