Nilpotent commutators and reducibility of semigroups
Date
-
Topic
Let f be a noncommutative polynomial in two variables. Let
mathcal{S} be a multiplicative semigroup of linear operators on a
finite-dimensional vector space and T a fixed linear operator such that
f(T,S)=0 for all S in mathcal{S}. What can we say about the invariant
subspace structure of mathcal{S}? We study special cases of this and
other related conditions.