Twisted sums of Banach and nuclear spaces

Domański, Paweł

doi:10.1090/S0002-9939-1986-0835872-2

Twisted sums of Banach and nuclear spaces
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Proc. Amer. Math. Soc. 97 (1986), 237-243 Request permission

Abstract:

A twisted sum of (topological vector) spaces $Y$ and $Z$ is a space $X$ with a subspace ${Y_1}$ isomorphic to $Y$ for which $X/{Y_1}$ is isomorphic to $Z$. It splits if ${Y_1}$ is complemented. It is proved that every twisted sum of a Banach space $Y$ and a nuclear space $Z$ splits. Köthe sequence spaces $Z$ for which this holds are characterized. Every locally convex twisted sum of a nuclear Fréchet space $Y$ and a Banach space $Z$ splits too. If $Z$ is superreflexive, then the local convexity assumption on the twisted sum may be omitted. Other results of this kind on Köthe sequence spaces are obtained.

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On the functors

for Fréchet spaces

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