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Every separable complex Fréchet space with a continuous norm is isomorphic to a space of holomorphic functions. (English) Zbl 1478.46003

J. Mashreghi and T. Ransford [Anal. Math. Phys. 9, No. 2, 899–905 (2019; Zbl 1416.41005)] have shown that every separable, infinite-dimensional, complex Banach space can be isometrically embedded into a Banach space of holomorphic functions. In the present paper, the analogue of this theorem for Fréchet spaces with continuous norm is shown. As in the case of Banach spaces, the proof relies on the construction of a suitable biorthogonal system.
This result implies that many counterexamples in the theory of Fréchet spaces can be realized as spaces of holomorphic functions.

MSC:

46A04 Locally convex Fréchet spaces and (DF)-spaces
46A32 Spaces of linear operators; topological tensor products; approximation properties
46E10 Topological linear spaces of continuous, differentiable or analytic functions

Citations:

Zbl 1416.41005
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References:

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