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Fernandez Unzueta, Maite and Prieto Yerro, M. Ángeles
(2010)
*Extension of polynomials defined on subspaces.*
Mathematical Proceedings of the Cambridge Philosophical Society, 148
(3).
pp. 505-518.
ISSN 0305-0041

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Official URL: http://journals.cambridge.org/abstract_S0305004110000022

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http://www.cambridge.org | Publisher |

## Abstract

Let k is an element of N and let E be a Banach space such that every k-homogeneous polynomial defined on a subspace of E has an extension to E. We prove that every norm one k-homogeneous polynomial, defined on a subspace, has an extension with a uniformly bounded norm. The analogous result for holomorphic functions of bounded type is obtained. We also prove that given an arbitrary subspace F subset of E. there exists a continuous morphism phi(k,F) : P((k)F) -> P((k)E) satisfying phi(k,F)(P)vertical bar(F) = P, if and only E is isomorphic to a Hilbert space.

Item Type: | Article |
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Uncontrolled Keywords: | Homogeneous polynomial; Holomorphic functions of bounded type; Extension theorems; Extension morphism |

Subjects: | Sciences > Mathematics > Functional analysis and Operator theory |

ID Code: | 17522 |

Deposited On: | 21 Dec 2012 11:52 |

Last Modified: | 07 Sep 2018 15:37 |

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