Every separable complex Fréchet space with a continuous norm is isomorphic to a space of holomorphic functions

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 examples of nuclear Fréchet spaces of holomorphic functions without the bounded approximation exist.

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