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Spectra of algebras of entire functions on Banach spaces

Author: Andriy Zagorodnyuk
Journal: Proc. Amer. Math. Soc. 134 (2006), 2559-2569
MSC (2000): Primary 46J15, 46J20; Secondary 46E15, 46E25, 46G20, 46G25
Published electronically: February 8, 2006
MathSciNet review: 2213733
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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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Additional Information

Andriy Zagorodnyuk
Affiliation: Institute for Applied Problems of Mechanics and Mathematics, Ukrainian Academy of Sciences, 3 b, Naukova str., Lviv 79060, Ukraine
Address at time of publication: Department of Mathematics and Statistics, McLean Hall, University of Saskatchewan, 106 Wiggins Road, Saskatoon, Saskatchewan, Canada S7N 5E6

Keywords: Infinite-dimensional holomorphy, spectra of algebras
Received by editor(s): July 8, 2004
Received by editor(s) in revised form: January 28, 2005, February 1, 2005, and March 15, 2005
Published electronically: February 8, 2006
Additional Notes: This research was supported in part by NSERC research grant OGP 005616.
Communicated by: N. Tomczak-Jaegermann
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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