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2 results

Every Separable Complex Fréchet Space with a Continuous Norm is Isomorphic to a Space of Holomorphic Functions
Part of
- Topological linear spaces and related structures
José Bonet
Journal:

Canadian Mathematical Bulletin / Volume 64 / Issue 1 / March 2021

Published online by Cambridge University Press:

13 March 2020, pp. 8-12

Print publication:

March 2021
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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.

The Fréchet Schwartz Algebra of Uniformly Convergent Dirichlet Series
Part of
José Bonet
Journal:

Proceedings of the Edinburgh Mathematical Society / Volume 61 / Issue 4 / November 2018

Published online by Cambridge University Press:

07 May 2018, pp. 933-942
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The algebra of all Dirichlet series that are uniformly convergent in the half-plane of complex numbers with positive real part is investigated. When it is endowed with its natural locally convex topology, it is a non-nuclear Fréchet Schwartz space with basis. Moreover, it is a locally multiplicative algebra but not a Q-algebra. Composition operators on this space are also studied.

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2 results

Every Separable Complex Fréchet Space with a Continuous Norm is Isomorphic to a Space of Holomorphic Functions

The Fréchet Schwartz Algebra of Uniformly Convergent Dirichlet Series