The maximal ideal space of <IMG ALIGN=MIDDLE HEIGHT=32 WIDTH=62> with respect to the Hadamard product期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

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The maximal ideal space of with respect to the Hadamard product

Authors:	Hermann Render

Institution:	Universität Duisburg, Fachbereich Mathematik, Lotharstr. 65, D-47057 Duisburg, Federal Republic of Germany

Abstract:	It is shown that the space of all regular maximal ideals in the Banach algebra $H^{\infty }(\mathbb{D} )$ with respect to the Hadamard product is isomorphic to $\mathbb{N} _{0}.$ The multiplicative functionals are exactly the evaluations at the -th Taylor coefficient. It is a consequence that for a given function $f(z) =\sum _{n=0}^{\infty }a_{n} z^{n}$ in $H^{\infty }(\mathbb{D} )$ and for a function holomorphic in a neighborhood of with and $a_{n} \in U$ for all $n \in \mathbb{N}_{0}$ the function $g(z) =\sum _{n=0}^{\infty }F(a_{n} ) z^{n}$ is in $H^{\infty }(\mathbb{D} ) .$

Keywords:	Hadamard product bounded analytic functions

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