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arXiv · 1905.10213

The invariant subspace problem for the space of smooth functions on the real line

Adam Przestacki·Michał Goliński
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Abstract

We construct a continuous linear operator acting on the space of smooth functions on the real line without non-trivial invariant subspaces. This is a first example of such an operator acting on a Fr\'echet space without a continuous norm. The construction is based on the ideas due to C. Read who constructed a continuous operator without non-trivial invariant subspaces on the Banach space $\ell_1$.

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Adam Przestacki, Michał Goliński. 2019-05-24. The invariant subspace problem for the space of smooth functions on the real line. https://arxiv.org/abs/1905.10213

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