Let U be an n-dimensional vector space over: a field of characteristic
O. For each positive integer k < min{m, n}, let J(k) be the set of al
l decomposable elements x(1) x ... x x(m) in the mth tensor product ci
rcle times(m) U such that dim(x(1),..., x(m)) less than or equal to k.
We characterize those nonsingular linear mappings T on x(m) U such th
at T(J(k)) subset of or equal to J(k). (C) 1997 Elsevier Science Inc.