Positive and real-positive solutions to the equation axa* = c in C*-algebras
D Cvetkovic-Ilic, Alegra Dajic, JJ Koliha
LINEAR & MULTILINEAR ALGEBRA | TAYLOR & FRANCIS LTD | Published : 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.