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Spectra of Algebras of Entire Functions on Banach Spaces

Andriy Zagorodnyuk
Proceedings of the American Mathematical Society
Vol. 134, No. 9 (Sep., 2006), pp. 2559-2569
Stable URL: http://www.jstor.org/stable/4098103
Page Count: 11
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Since scans are not currently available to screen readers, please contact JSTOR User Support for access. We'll provide a PDF copy for your screen reader.
Spectra of Algebras of Entire Functions on Banach Spaces
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Abstract

We obtain an explicit description of the spectrum (set of closed maximal ideals) of $H_{b}(X)$, algebra of analytic functions on a Banach space X which are bounded on bounded subsets. We show that the spectrum of $H_{b}(X)$ admits a natural linear structure. Some applications to the algebra of uniformly continuous and bounded analytic functions on the unit ball $B \subset X$ are indicated.

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