Interpolation problem for $\ell^1$ and a uniform algebra

J. Austral. Math. Soc. 72 (2002), 1-11

Takahiko Nakazi
Department of Mathematics
Hokkaido University
Sapporo 060-0810
Japan
nakazi@math.sci.hokudai.ac.jp

Abstract

Let A be a uniform algebra and M(A) the maximal ideal space of A. A sequence $\{a_n\}$ in M(A) is called $\ell^1$ -interpolating if for every sequence $(\alpha_n)$ in $\ell^1$ there exists a function f in A such that $f(a_n) = \alpha_n$ for all n. In this paper, an $\ell^1$ -interpolating sequence is studied for an arbitrary uniform algebra. For some special uniform algebras, an $\ell^1$ -interpolating sequence is equivalent to a familiar $\ell^\infty$ -interpolating sequence. However, in general these two interpolating sequences may be different from each other.

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