An application of grand Furuta inequality to a type of operator equation

Copyright c©2014 Jian Shi. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. The existence of positive semidefinite solutions of the operator equation n∑ j=1 An−jXAj−1 = Y is investigated by applying grand Furuta inequality. If there exists positive semidefinite solutions of the operator equation, one of the special types of Y is obtained, which extends the related result before. Finally, an example is given based on our result