On non-Archimedean Fréchet spaces with nuclear Köthe quotients

Śliwa, Wiesław

doi:10.1090/S0002-9947-10-05033-6

On non-Archimedean Fréchet spaces with nuclear Köthe quotients
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Trans. Amer. Math. Soc. 362 (2010), 3273-3288 Request permission

Abstract:

Assume that $\mathbb {K}$ is a complete non-Archimedean valued field. We prove that every infinite-dimensional Fréchet-Montel space over $\mathbb {K}$ which is not isomorphic to $\mathbb {K}^{\mathbb {N}}$ has a nuclear Köthe quotient. If the field $\mathbb {K}$ is non-spherically complete, we show that every infinite-dimensional Fréchet space of countable type over $\mathbb {K}$ which is not isomorphic to the strong dual of a strict $LB$-space has a nuclear Köthe quotient.

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