Inequalities for norms on products of star ordered operators

• Cristina Cano ^[1] ; Irene Mosconi ^[1] ; Susana Nicolet ^[1]
  1. [1] Universidad Nacional del Comahue

     Universidad Nacional del Comahue

     Argentina

     
• Localización: Revista de la Unión Matemática Argentina, ISSN 0041-6932, ISSN-e 1669-9637, Vol. 53, Nº. 1, 2012, págs. 93-100
• Idioma: inglés
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• Resumen

  • The aim of this paper is to relate the star order in operators in a Hilbert space with certain norm inequalities. We are showing inequalities of the type ‖BXA‖2 ≤ ‖XBA‖2 (or ‖BXA2‖ ≥ ‖XBA‖2), which are already known under the assumption that A = ψ(B), with ψ a positive increasing (or decreasing, respectively) function defined on the spectrum of B. In this work, we will study this type of inequalities with the hypothesis that A ≤∗ B, where A ≤∗ B if A∗A = B∗A and AA∗ = BA∗.