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oai:docta.ucm.es:20.500.14352/424572023-08-27T15:04:31Zcom_20.500.14352_14col_20.500.14352_15

Extension of polynomials defined on subspaces. Fernandez Unzueta, Maite Prieto Yerro, M. Ángeles 517.98 Homogeneous polynomial Holomorphic functions of bounded type Extension theorems Extension morphism Análisis funcional y teoría de operadores 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. CONACyT MEC UCM Depto. de Álgebra, Geometría y Topología Fac. de Ciencias Matemáticas TRUE pub 2023-06-20T00:21:47Z 2023-06-20T00:21:47Z 2010 journal article https://hdl.handle.net/20.500.14352/42457 0305-0041 10.1017/S0305004110000022 eng P48363-F MTM 2006-03531 910626. restricted access application/pdf Cambridge Univ Press