J. Austral. Math. Soc.  72 (2002), 1-11
Interpolation problem for $\ell^1$ and a uniform algebra

Takahiko Nakazi
  Department of Mathematics
  Hokkaido University
  Sapporo 060-0810

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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