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

 

Extendibility of homogeneous polynomials
on Banach spaces


Authors: Pádraig Kirwan and Raymond A. Ryan
Journal: Proc. Amer. Math. Soc. 126 (1998), 1023-1029
MSC (1991): Primary 46G20; Secondary 46B28
MathSciNet review: 1415346
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Abstract: We study the $n$-homogeneous polynomials on a Banach space $X$ that can be extended to any space containing $X$. We show that there is an upper bound on the norm of the extension. We construct a predual for the space of all extendible $n$-homogeneous polynomials on $X$ and we characterize the extendible 2-homogeneous polynomials on $X$ when $X$ is a Hilbert space, an $\mathcal L_1$-space or an $\mathcal L_\infty$-space.


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Additional Information

Pádraig Kirwan
Affiliation: Department of Mathematics, University College, Galway, Ireland
Address at time of publication: Department of Physical and Quantitative Sciences, Waterford Institute of Technology, Waterford, Ireland
Email: pkirwan@staffmail.wit.ie

Raymond A. Ryan
Affiliation: Department of Mathematics, University College, Galway, Ireland
Email: ray.ryan@ucg.ie

DOI: http://dx.doi.org/10.1090/S0002-9939-98-04009-X
PII: S 0002-9939(98)04009-X
Keywords: Homogeneous polynomial, extendibility
Received by editor(s): May 17, 1996
Received by editor(s) in revised form: July 10, 1996
Communicated by: Theodore W. Gamelin
Article copyright: © Copyright 1998 American Mathematical Society