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Interpolation problem for l1 and a uniform algebra

Part of: Commutative Banach algebras and commutative topological algebras

Published online by Cambridge University Press:  09 April 2009

Takahiko Nakazi
Takahiko Nakazi
Affiliation:
Department of Mathematics, Hokkaido University, Sapporo 060-0810, Japan e-mail: nakazi@math.sci.hokudai.ac.jp
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Abstract

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Let A be a uniform algebra and M(A) the maximal ideal space of A. A sequence {an} in M(A) is called l1-interpolating if for every sequence (αn) in l1 there exists a function f in A such that f (an) = αn for all n. In this paper, an l1-interpolating sequence is studied for an arbitrary uniform algebra. For some special uniform algebras, an l1-interpolating sequence is equivalent to a familiar l-interpolating sequence. However, in general these two interpolating sequences may be different from each other.

Keywords

uniform algebrallnterpolationmaximal ideal spacepseudo-hyperbolic distance

MSC classification

Secondary: 46J10: Banach algebras of continuous functions, function algebras 46J15: Banach algebras of differentiable or analytic functions, $H^p$-spaces
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 72 , Issue 1 , February 2002 , pp. 1 - 12
Copyright
Copyright © Australian Mathematical Society 2002

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