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Every Separable Complex Fréchet Space with a Continuous Norm is Isomorphic to a Space of Holomorphic Functions
Published online by Cambridge University Press: 13 March 2020
Abstract
Extending a result of Mashreghi and Ransford, we prove that every complex separable infinite-dimensional Fréchet space with a continuous norm is isomorphic to a space continuously included in a space of holomorphic functions on the unit disc or the complex plane, which contains the polynomials as a dense subspace. As a consequence, we deduce the existence of nuclear Fréchet spaces of holomorphic functions without the bounded approximation.
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- © Canadian Mathematical Society 2020
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