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Analytic functions on $$c_ 0$$. (English) Zbl 0748.46021
Summary: Let $$F$$ be a space of continuous complex valued functions on a subset of $$c_ 0$$ which contains the standard unit vector basis $$\{e_ n\}$$. Let $$R:F\to C^ N$$ be the restriction map, given by $$R(f)=(f(e_ 1),\dots,f(e_ n),\dots)$$. We characterize the ranges $$R(F)$$ for various “nice” spaces $$F$$. For example, if $$F=P(^ nc_ 0)$$, then $$R(F)=\ell_ 1$$, and if $$F=A^ \infty(B(c_ 0))$$, then $$R(F)=\ell_ \infty$$.

##### MSC:
 46G20 Infinite-dimensional holomorphy 46E50 Spaces of differentiable or holomorphic functions on infinite-dimensional spaces 47A05 General (adjoints, conjugates, products, inverses, domains, ranges, etc.) 46A45 Sequence spaces (including Köthe sequence spaces)
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