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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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