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

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 Fréchet 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 ${\ell }_1$.

References in corpus (1)

• Invariant subspaces for non-normable Fréchet spaces