The invariant subspace problem for the space of smooth functions on the real line
Functional Analysis
2019-05-27 v1
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 .
Keywords
Cite
@article{arxiv.1905.10213,
title = {The invariant subspace problem for the space of smooth functions on the real line},
author = {Adam Przestacki and Michał Goliński},
journal= {arXiv preprint arXiv:1905.10213},
year = {2019}
}