On 2-Homogeneous Polynomials on Some Non-stable Banach and Fréchet Spaces
✍ Scribed by Juan Carlos Dı́az
- Publisher
- Elsevier Science
- Year
- 1997
- Tongue
- English
- Weight
- 152 KB
- Volume
- 206
- Category
- Article
- ISSN
- 0022-247X
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✦ Synopsis
Let F be a Banach or a nuclear Frechet space isomorphic to its square. Then Ž2 . P F , the space of 2-homogeneous polynomials on F, is isomorphic to the space Ž . of continuous linear operators L F, FЈ , both of them endowed with the topology of uniform convergence on bounded sets. In this note we prove that the isomorphism can fail if F is not stable by studying two kind of examples: First, for Banach spaces, we consider James spaces J constructed with the l -norm, with p ) 2; p p second, we treat nuclear power spaces of finite or infinite type. ᮊ 1997 Academic Press Ž . Given a real or complex Frechet space F we denote by F m F the ´ completed projective tensor product of F with itself. The symmetric ˆs projective tensor product, denoted by F m F, is the closed subspace of *The research of the author has been partially supported by the DGICYT project