Positive and real-positive solutions to the equationaxa*=cinC*-algebras
Dragana S. Cvetković‐Ilić, Alegra Dajić, J. J. Koliha · Linear and Multilinear Algebra · 2007
We obtain new representations for the general positive and real-positive solutions of the equation axa*=c in a C*-algebra using the characterization of positivity based on a matrix representation of an element and the generalized Schur complement. Applications to the equation AXA*=C for operators between Hilbert spaces and for finite matrices are given.