A Note on Semigroups of Linear Transformations with Invariant Subspaces
Pei Huisheng, Xinyang Henan · 2012
Let V be a vector space over a field and T(V ) the semigroup of all linear transformations from V into V . For a fixed subspace W of V , denote S(V, W )= {α ∈ T(V ): Wα ⊆ W }. Then S(V, W) is a subsemigroup of T(V ). In this note, we show that the semigroup S(V, W) is always abundant.