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Extendible Polynomials on Banach Spaces

✍ Scribed by Daniel Carando

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
114 KB
Volume
233
Category
Article
ISSN
0022-247X

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✦ Synopsis

We are concerned with the following question: when can a polynomial P:

Ž . E ª X E and X are Banach spaces be extended to a Banach space containing E? We prove that the polynomials that are extendible to any larger space are Ž X . precisely those which can be extended to C B , if X is complemented in its E Ž X . bidual, and l B in general. We also show that the extendibility is a property that ϱ E is preserved by Aron᎐Berner extensions and composition with linear operators. We construct a predual of the space of extendible polynomials for the case that X is a dual space.

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