Decompositions of Montel Köthe sequence spaces


The following result has been recently proved by the author: Let E be a Fréchet Schwartz space with unconditional basis and with continuous norm; let F be any infinite dimensional subspace of E. Then we can write E as G⨂ H where G and H do not have any subspace isomorphic to F. This theorem is extended here in two directions: (i)If E is a Montel Köthe sequence space (with certain additional assumptions which are satisfied by the examples described in the literature) and the subspace F is Montel non-Schwartz; (ii) If E is any Fréchet Schwartz space with unconditional basis (so the existence of continuous norm is dropped) and F is not isomorphic to ω.

DOI Code: 10.1285/i15900932v17p143

Keywords: Köthe sequence spaces; Primary spaces; Complemented subspaces; Countable products of Fréchet Schwartz spaces

Classification: 46A45; 46A01; 46A11

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