Abstract
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 Fréchet nuclear spaces with bases E and F so that τ o =τ ω on
Acknowledgement
The author wishes to thank the referee for his/her helpful comments and suggestions.
Notes
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