Invariant subspaces for Fréchet spaces without continuous norm

Menet, Quentin

doi:10.1090/proc/15418

Invariant subspaces for Fréchet spaces without continuous norm
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by Quentin Menet PDF

Proc. Amer. Math. Soc. 149 (2021), 3379-3393 Request permission

Abstract:

Let $(X,(p_j))$ be a Fréchet space with a Schauder basis and without continuous norm, where $(p_j)$ is an increasing sequence of seminorms inducing the topology of $X$. We show that $X$ satisfies the Invariant Subspace Property if and only if there exists $j_0\ge 1$ such that $\ker p_{j+1}$ is of finite codimension in $\ker p_{j}$ for every $j\ge j_0$.

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