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
Full Text: DOI


[1] Gamelin, T., Uniform algebras (1984), New York: Chelsea, New York · Zbl 0213.40401
[2] Seddighi, K.; Hedayatiyan, K.; Yousefi, B., Operators acting on certain Banach spaces of analytic functions, International Journal of Mathematics and Mathematical Sciences, 18, 107-110 (1995) · Zbl 0821.47022 · doi:10.1155/S0161171295000147
[3] Shields, A. L., Weighted shift operators and analytic function theory, Math. Survey, A.M.S. Providence, 13, 49-128 (1974) · Zbl 0303.47021
[4] Yousefi, B., On the space ℓ^p(β), Rend. Circ. Mat. Palermo, 49, 115-120 (2000) · Zbl 0952.47027 · doi:10.1007/BF02904223
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.