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Extension of polynomials defined on subspaces
| Content Provider | Scilit |
|---|---|
| Author | Fernández-Unzueta, Maite Prieto, Ángeles |
| Copyright Year | 2010 |
| Description | 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 $φ_{k, F}$: $(^{k}$F) → $(^{k}$E) satisfying $φ_{k, F}(P)_{|F}$ = P, if and only E is isomorphic to a Hilbert space. |
| Related Links | http://pdfs.semanticscholar.org/2bdf/42d0376e405127d1e5b77e683f677cc3b9be.pdf https://www.cambridge.org/core/services/aop-cambridge-core/content/view/7872AD36BE7E22C14C461B319208623F/S0305004110000022a.pdf/div-class-title-extension-of-polynomials-defined-on-subspaces-div.pdf |
| Ending Page | 518 |
| Page Count | 14 |
| Starting Page | 505 |
| ISSN | 03050041 |
| e-ISSN | 14698064 |
| DOI | 10.1017/s0305004110000022 |
| Journal | Mathematical Proceedings of the Cambridge Philosophical Society |
| Issue Number | 3 |
| Volume Number | 148 |
| Language | English |
| Publisher | Cambridge University Press (CUP) |
| Publisher Date | 2010-05-01 |
| Access Restriction | Open |
| Subject Keyword | Mathematical Proceedings of the Cambridge Philosophical Society Applied Mathematics Polynomials Defined |
| Content Type | Text |
| Resource Type | Article |
| Subject | Mathematics |
