Polynomially significant properties and equivalence of topologies on fully nuclear spaces
Titel:
Polynomially significant properties and equivalence of topologies on fully nuclear spaces
Auteur:
Boyd, Christopher
Verschenen in:
Complex variables and elliptic equations
Paginering:
Jaargang 49 (2004) nr. 10 pagina's 739-745
Jaar:
2004-08-15
Inhoud:
We relate the equivalence of the topologies τ o and τ ω on a fully nuclear space E having the bounded approximation property with the polynomially significant properties on E'b, using the localization property of Defant and Govaerts (A. Defant and W. Govaerts (1986). Tensor products and spaces of vector-valued continuous functions. Manuscripta Math., 55, 433-449). This allows us to give examples of Frechet nuclear spaces with bases E and F so that τ o=τ ω on [image omitted]. We also give an example of Frechet nuclear spaces with bases E and F so that τ o=τ ω on [image omitted] for every open polydisc U in E× F']. The conditions for equivalence of topologies are expressed in terms of the linear invariants (DN), [image omitted] and [image omitted] given in Vogt (D. Vogt (1983). Frechetraume, zwischen denen jede stetige lineare Abbildung beschrankt ist. J. reine u. angew. Math., 345, 182-200.) and Meise and Vogt (R. Meise and D. Vogt (1986). Holomorphic functions of uniformly bounded type on nuclear Frechet spaces. Studia Math., 83, 147-175.).
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