RT Journal Article
T1 Extension of polynomials defined on subspaces.
A1 Fernandez Unzueta, Maite
A1 Prieto Yerro, M. Ángeles
AB 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.
PB Cambridge Univ Press
SN 0305-0041
YR 2010
FD 2010
LK https://hdl.handle.net/20.500.14352/42457
UL https://hdl.handle.net/20.500.14352/42457
LA eng
NO CONACyT
NO MEC
NO UCM
DS Docta Complutense
RD 6 abr 2025