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Extension of polynomials defined on subspaces.

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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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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
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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