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arXiv · 1812.11091

A characterization of maximal ideals in the Fr\'{e}chet algebras of holomorphic functions $F^p$ $(1<p<\infty$

Romeo Meštrović
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Abstract

The space $F^p$ ($1 0}$ defined for $f\in F^q$ as $\Vert f\Vert_{q,c}:=\sum_{n=0}^{\infty}\vert a_n\vert\exp\left(-cn^{1/(q+1)} \right)<\infty,$ is a countably normed Fr\'{e}chet algebra. Notice that for each $p>1$, $F^p$ is the Fr\'{e}chet envelope of the Privalov space $N^p$. In this paper we study the structure of maximal ideals in the algebras $F^p$ ($1<p<\infty$). In particular, we give a complete characterization of closed maximal ideals in $F^p$. Moreover, we characterize multiplicative linear functionals on $F^p$.

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BibTeXRIS

Romeo Meštrović. 2018-12-25. A characterization of maximal ideals in the Fr\'{e}chet algebras of holomorphic functions $F^p$ $(1<p<\infty$. https://arxiv.org/abs/1812.11091

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