Infinite dimensional linear groups with a spacious family of $G$-invariant subspaces - A. V. Sadovnichenko (Математичні Студії, 2013)
Let $F$ be a field, $A$ be a vector space over $F$, $GL (F, A)$ be the group of all automorphisms of the vector space $A$. If $B leq A$ then denote by $mathopm Core_G (B)$ the largest $G$-invariant subspace of~$B$. A subspace $B$ is called almost $G$-invariant if $mathopm dim_F (B/mathopm Core_G (B))$ is finite. In this paper we described the {case where} every subspace of $A$ is almost $G$-invariant.