Every Separable Complex Fréchet Space with a Continuous Norm is Isomorphic to a Space of Holomorphic Functions. Issue 1 (13th March 2021)

• Record Type: Journal Article
• Authors: Bonet, José
• Is Part Of: Canadian mathematical bulletin =. Volume 64:Issue 1(2021)
• Page Start: 8
• Page End: 12
• Publication Date: 2021-03-13
• Subjects: 46A04, -- 46A11, -- 46A32; Spaces of holomorphic functions, -- Fréchet spaces, -- continuous norm, -- bounded approximation property; Mathematics -- Periodicals; Mathematics; Periodicals; 510.5
• DOI: 10.4153/S000843952000017X
• Languages: English
• ISSNs: 0008-4395

Abstract

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.