On 2-homogeneous polynomials on some non-stable Banach and Frechet spaces

[摘要] Let F be a Banach or a nuclear Frechet space isomorphic to its square. Then P(F-2), the space of 2-homogeneous polynomials on F, is isomorphic to the space of continuous linear operators L(F, F'), 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(p) constructed with the l(p)-norm, with p > 2; second, we treat nuclear power spaces of finite or infinite type. (C) 1997 Academic Press.

[发布日期] 1997-02-01