Let X, Y be a pair of vector spaces over a field F associated with a bilinear form (,) such that (x, y) = 0 for all y in Y, implies that x = 0. Let (X ⊗ Y)0 be the subspace of X ⊗ Y spanned by all decomposable elements x ⊗ y with (x, y) = 0. Let U, V be any two vector spaces over F. In this note, we study linear mappings from (X ⊗ Y)0 to U ⊗ V that send nonzero decomposable elements to nonzero decomposable elements and some of its consequences. © 2009 Elsevier Inc. All rights reserved.
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