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Positive and real-positive solutions to the equation axa*=c in C*-algebras |
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| Authors: | D Cvetković-Ilić Alegra Dajić |
| Institution: | 1. Faculty of Mathematics and Sciences , University of Ni? , Vi?egradska 33, 18000 Ni?, Serbia;2. Department of Mathematics and Statistics , University of Melbourne , Melbourne, VIC 3010, Australia |
| Abstract: | 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. |
| Keywords: | C*-algebra Regular element Moore-Penrose inverse Equation in a C*-algebra Positive solution Real-positive solution Hilbert space Operator equation Matrix equation |