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Spectra of algebras of entire functions on Banach spaces
Author(s):
Andriy
Zagorodnyuk
Journal:
Proc. Amer. Math. Soc.
134
(2006),
2559-2569.
MSC (2000):
Primary 46J15, 46J20;
Secondary 46E15, 46E25, 46G20, 46G25
Posted:
February 8, 2006
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Abstract:
We obtain an explicit description of the spectrum (set of closed maximal ideals) of  algebra of analytic functions on a Banach space  which are bounded on bounded subsets. We show that the spectrum of  admits a natural linear structure. Some applications to the algebra of uniformly continuous and bounded analytic functions on the unit ball  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
Email:
zahorodn@math.usask.ca, andriyzag@yahoo.com
DOI:
10.1090/S0002-9939-06-08260-8
PII:
S 0002-9939(06)08260-8
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
Posted:
February 8, 2006
Additional Notes:
This research was supported in part by NSERC research grant OGP 005616.
Communicated by:
N. Tomczak-Jaegermann
Copyright of article:
Copyright
2006,
American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.
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