%0 Journal Article
%A Fernandez Unzueta, Maite
%A Prieto Yerro, M. Ángeles
%T Extension of polynomials defined on subspaces.
%D 2010
%@ 0305-0041
%U https://hdl.handle.net/20.500.14352/42457
%X 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.
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