Extendibility of homogeneous polynomials on Banach spaces
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- by Pádraig Kirwan and Raymond A. Ryan PDF
- Proc. Amer. Math. Soc. 126 (1998), 1023-1029 Request permission
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.References
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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
- Received by editor(s): May 17, 1996
- Received by editor(s) in revised form: July 10, 1996
- Communicated by: Theodore W. Gamelin
- © Copyright 1998 American Mathematical Society
- 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