Resumen de Inequalities for norms on products of star ordered operators

Cristina Cano, Irene Mosconi, Susana Nicolet

• 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∗.