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arXiv · 2002.12677

Every separable complex Fr\'echet space with a continuous norm is isomorphic to a space of holomorphic functions

José Bonet
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Abstract

Extending a result of Mashreghi and Ransford, we prove that every complex separable infinite dimensional Fr\'echet 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 Fr\'echet spaces of holomorphic functions without the bounded approximation exist.

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José Bonet. 2020-02-28. Every separable complex Fr\'echet space with a continuous norm is isomorphic to a space of holomorphic functions. https://doi.org/10.4153/s000843952000017x

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