Bounded analytic structure of the Banach space of formal power series. (English) Zbl 1194.47035

Summary: Let \(\{ \beta (n)\} _{n = 0}^\infty \) be a sequence of positive numbers and \(1\leq p< \infty\). We consider the space \(H^p(\beta)\) of all power series \(f(z) = \sum_{n = 0}^\infty \hat{f}(n)z^n \) such that \(\sum |\hat{f}(n)|^p \beta (n)^p< \infty \). We investigate regions on which our formal power series represent bounded analytic functions.


47B37 Linear operators on special spaces (weighted shifts, operators on sequence spaces, etc.)
47A25 Spectral sets of linear operators
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