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A monomial basis for the holomorphic functions on 
Authors:
Seán Dineen and Jorge Mujica
Journal:
Proc. Amer. Math. Soc. 141 (2013), 1663-1672
MSC (2010):
Primary 46G20, 32A05
Posted:
November 2, 2012
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Abstract: For over thirty years it has been known that the monomials form a basis for the  -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  , 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
Posted:
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.
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