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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Vector spaces of entire functions of unbounded type


Author: Jerónimo López - Salazar Codes
Journal: Proc. Amer. Math. Soc. 139 (2011), 1347-1360
MSC (2010): Primary 46G20; Secondary 46E50
Published electronically: November 23, 2010
MathSciNet review: 2748427
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Abstract: Let $ E$ be an infinite dimensional complex Banach space. We prove the existence of an infinitely generated algebra, an infinite dimensional closed subspace and a dense subspace of entire functions on $ E$ whose non-zero elements are functions of unbounded type. We also show that the $ \tau_{\delta }$ topology on the space of all holomorphic functions cannot be obtained as a countable inductive limit of Fréchet spaces.


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Additional Information

Jerónimo López - Salazar Codes
Affiliation: Departamento de Análisis Matemático, Universidad Complutense de Madrid, 28040 Madrid, Spain
Email: jlopezsalazar@mat.ucm.es

DOI: http://dx.doi.org/10.1090/S0002-9939-2010-10817-1
PII: S 0002-9939(2010)10817-1
Keywords: Entire function, \it lineable set, $\tau_{\delta}$ topology
Received by editor(s): February 22, 2010
Received by editor(s) in revised form: April 7, 2010
Published electronically: November 23, 2010
Additional Notes: The author was supported by UCM Grant #BE46/08.
Communicated by: Mei-Chi Shaw
Article copyright: © Copyright 2010 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.