Invertible preservers of certain decomposable tensors (Q1372966)

Let \(U\) be an \(n\)-dimensional vector space over a field of characteristic \(0\). For each positive integer \(k<\min\{m, n\}\) let \(J_k\) be the set of all decomposable elements \(x_1\otimes\cdots\otimes x_m\) in the \(m\)th tensor product \(\overset {m}\otimes U\) such that \(\dim\langle x_1,\dots, x_m\rangle\leq k\). The author characterizes those nonsingular linear mappings \(T\) on \(\overset {m}\otimes U\) such that \(T(J_k)\subseteq J_k\). The paper contains three major theorems.