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Extension of polynomials defined on subspaces
Published online by Cambridge University Press: 16 March 2010
Abstract
Let k ∈ 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 ⊂ E, there exists a continuous morphism φk, F: (kF) → (kE) satisfying φk, F(P)|F = P, if and only E is isomorphic to a Hilbert space.
- Type
- Research Article
- Information
- Mathematical Proceedings of the Cambridge Philosophical Society , Volume 148 , Issue 3 , May 2010 , pp. 505 - 518
- Copyright
- Copyright © Cambridge Philosophical Society 2010
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