Bilinear forms on matrix algebras vanishing on zero products of xy and yx

Kosan M. T., Lee T., Zhou Y.

LINEAR ALGEBRA AND ITS APPLICATIONS, cilt.453, ss.110-124, 2014 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 453
  • Basım Tarihi: 2014
  • Doi Numarası: 10.1016/j.laa.2014.04.004
  • Dergi Adı: LINEAR ALGEBRA AND ITS APPLICATIONS
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Sayfa Sayıları: ss.110-124
  • Anahtar Kelimeler: Matrix algebra, n-Linear form, Zero product, Reduced trace, Elementary operator, GENERALIZED SKEW DERIVATIONS, OPERATOR-ALGEBRAS, JORDAN PRODUCTS, LIE DERIVATIONS, ADDITIVE MAPS, NEST-ALGEBRAS, PRIME-RINGS
  • Gazi Üniversitesi Adresli: Hayır

Özet

Let D be a division algebra finite-dimensional over its center C, Omega := M-m(D), the m x m matrix algebra over D, and V be a vector space over C. We characterize all n-linear forms on Omega in terms of reduced traces and elementary operators. For m > 1, it is proved that a bilinear form B: Omega x Omega -> V vanishes on zero products of xy and yx if and only if there exist linear maps g, h: Omega -> V such that B(x, y) = g(xy) + h(yx) for all x, y is an element of Omega. As an application, a bilinear form B is completely characterized if B(x, y) = 0 whenever x, y is an element of Omega satisfy xy + xi yx = 0, where xi is a fixed nonzero element in C. (C) 2014 Elsevier Inc. All rights reserved.