Vol. 102, No. 1, 1982

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ISSN: 0030-8730
Interpolation in strongly logmodular algebras

Rahman Mahmoud Younis

Vol. 102 (1982), No. 1, 247–251
Abstract

Let A be a strongly logmodular subalgebra of C(X), where X is a totally disconnected compact Hausdorff space. For s a weak peak set for A, define As = {f C(X) : f|s A|s}. We prove the following:

Theorem1. Let s be a weak peak set for A. If b is an inner function such that b|s is invertible in A|s then there exists a function F in A C(X)1 such that F = b on s.

Theorem 2. Let s be a weak peak set for A. If U C(X), |U| = 1 on s and dist(U,As) < 1, then there exists a unimodular function Ũ in C(X) such that Ũ = U on s and dist(Ũ,A) < 1.

Mathematical Subject Classification 2000
Primary: 46J10
Milestones
Received: 5 May 1980
Published: 1 September 1982
Authors
Rahman Mahmoud Younis