Algebras of Bounded Analytic Functions containing the Disk Algebra

Izuchi, Keiji ; Izuchi, Yuko

Canadian journal of mathematics, Tome 38 (1986) no. 1, pp. 87-108

Résumé

Let D be the open unit disk and let ∂D be its boundary. We denote by C the algebra of continuous functions on ∂d, and by L∞ the algebra of essentially bounded measurable functions with respect to the normalized Lebesgue measure m on ∂D. Let H ∞ be the algebra of bounded analytic functions on D. Identifying with their boundary functions, we regard H ∞ as a closed subalgebra of L ∞. Let A = H ∞ Pi C, which is called the disk algebra. The algebras A and H ∞ have been studied extensively [5, 6, 7]. In these fifteen years, norm closed subalgebras between H ∞ and L ∞, called Douglas algebras, have received considerable attention in connection with Toeplitz operators [12]. A norm closed subalgebra between A and H ∞ is called an analytic subalgebra. In [2], Dawson studied analytic subalgebras and he remarked that there are many different types of analytic subalgebras. One problem is to study which analytic subalgebras are backward shift invariant. Here, a subset E of H ∞ is called backward shift invariant if

Détail

DOI : 10.4153/CJM-1986-005-9

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