Some remarks on invariant subspaces in real Banach spaces (revised version)
Functional Analysis
2022-09-23 v1
Abstract
It is proved that a commutative algebra of operators on a reflexive real Banach space has an invariant subspace if each operator satisfies the condition where is the essential norm. This implies the existence of an invariant subspace for every commutative family of essentially selfadjoint operators on a real Hilbert space.
Cite
@article{arxiv.2209.10921,
title = {Some remarks on invariant subspaces in real Banach spaces (revised version)},
author = {V. I. Lomonosov and V. S. Shulman},
journal= {arXiv preprint arXiv:2209.10921},
year = {2022}
}