INVERTIBLE PRESERVERS OF CERTAIN DECOMPOSABLE TENSORS

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.