@article{Emenyu_2016, title={An invariant subspace problem for multilinear operators on finite dimensional spaces}, volume={44}, url={https://apcz.umk.pl/TMNA/article/view/TMNA.2014.032}, abstractNote={We introduce the notion of invariant subspaces
for multilinear operators from which the invariant
subspace problems for multilinear and polynomial
operators arise. We prove that polynomial
operators acting in a finite dimensional complex
space and even polynomial operators acting in a
finite dimensional real space have eigenvalues.
These results enable us to prove that polynomial
and multilinear operators acting in a finite
dimensional complex space, even polynomial and
even multilinear operators acting in a finite
dimensional real space have nontrivial invariant
subspaces. Furthermore, we prove that odd polynomial
operators acting in a finite dimensional real space
either have eigenvalues or are homotopic to scalar
operators; we then use this result to prove that odd
polynomial and odd multilinear operators acting in a
finite dimensional real space may or may not have
invariant subspaces.}, number={1}, journal={Topological Methods in Nonlinear Analysis}, author={Emenyu, John}, year={2016}, month={Apr.}, pages={1–10} }