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

 

A monomial basis for the holomorphic functions on $ c_{0}$


Authors: Seán Dineen and Jorge Mujica
Journal: Proc. Amer. Math. Soc. 141 (2013), 1663-1672
MSC (2010): Primary 46G20, 32A05
Published electronically: November 2, 2012
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Abstract: For over thirty years it has been known that the monomials form a basis for the $ n$-homogeneous polynomials on certain infinite dimensional Banach spaces. Recently, Defant and Kalton have shown that these are never unconditional. In this article we show that the monomials form a basis for both the holomorphic functions and the holomorphic functions of bounded type on $ c_{0}$, both with their natural topologies.


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Additional Information

Seán Dineen
Affiliation: School of Mathematical Sciences, University College Dublin, Dublin 4, Ireland
Email: sean.dineen@ucd.ie

Jorge Mujica
Affiliation: IMECC-UNICAMP, Rua Sergio Buarque de Holanda 651, 13083-859 Campinas, SP, Brazil
Email: mujica@ime.unicamp.br

DOI: http://dx.doi.org/10.1090/S0002-9939-2012-11436-4
PII: S 0002-9939(2012)11436-4
Keywords: Holomorphic function, Schauder basis, monomial
Received by editor(s): March 4, 2011
Received by editor(s) in revised form: July 5, 2011, and September 6, 2011
Published electronically: November 2, 2012
Communicated by: Thomas Schlumprecht
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.