Vector spaces of entire functions of unbounded type
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- by Jerónimo López - Salazar Codes PDF
- Proc. Amer. Math. Soc. 139 (2011), 1347-1360 Request permission
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.References
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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
- 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
- © Copyright 2010
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 139 (2011), 1347-1360
- MSC (2010): Primary 46G20; Secondary 46E50
- DOI: https://doi.org/10.1090/S0002-9939-2010-10817-1
- MathSciNet review: 2748427