Linear rank one preservers between spaces of matrices with zero trace

  • Lim M
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Abstract

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.

Author-supplied keywords

  • Linear preserver
  • Rank one nilpotent
  • Tensor product

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Authors

  • Ming Huat Lim

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