Numerical range of a pair of strictly upper triangular matrices

• Yan, Wen ^[1]
  1. [1] Tuskegee University

     Tuskegee University

     Estados Unidos

     
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 30, Nº. 1, 2011, págs. 77-90
• Idioma: inglés
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• Resumen

  • Given two strictly upper triangular matrices X, Y ? Cm×m, we study the range WY (X) = {trnXn-1Y* : n ? N}, where N is the group of unit upper triangular matrices in Cm×m. We prove that it is either a point or the whole complex plane. We characterize when it is a point. We also obtain some convexity result for a similar range, where N is replaced by any ball of Ck(k = m(m - 1)/2) embedded in N , m = 4.