Polynomials and holomorphic functions on interpolation spaces. (English) Zbl 0709.46026

The author considers continuous injections of Banach spaces \(E_ 0\hookrightarrow E\hookrightarrow E_ 1\) and the extent to which holomorphic functions on \(E_ 1\) are uniformly bounded on E as a result of assumptions (of the interpolation type) concerning the injection \(E_ 0\hookrightarrow E_ 1.\)
The following is a typical result: If f is holomorphic on \(c_ 0\) and \(f|_{\ell_ 1}\) is of uniformly bounded type then \(f|_{\ell_ p}\) is also of uniformly bounded type for any p, \(1<p<\infty\).
Reviewer: S.Dineen


46G20 Infinite-dimensional holomorphy
46M35 Abstract interpolation of topological vector spaces
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