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

DOI:
https://doi.org/10.1090/S0002-9939-98-04009-X

MathSciNet review:
1415346

Full-text PDF

Abstract | References | Similar Articles | Additional Information

Abstract: We study the -homogeneous polynomials on a Banach space that can be extended to any space containing . We show that there is an upper bound on the norm of the extension. We construct a predual for the space of all extendible -homogeneous polynomials on and we characterize the extendible 2-homogeneous polynomials on when is a Hilbert space, an -space or an -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:
https://doi.org/10.1090/S0002-9939-98-04009-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