算子方程X^s-A~*X^(-t)A=I的正解

Positive solutions to operator equation X^s-A~*X^(-t)A=I

研究无限维复可分的Hilbert空间上算子方程Xs-A*X-tA=I(0<s<t)的正解问题,利用算子理论和迭代方法给出其有正解的一些必要条件和充分条件,特别地给出当A是正规算子,且t=2 ms(m为正整数)时该方程有正解的两个充分条件.

The problem of positive solutions to the operator equation Xs-A＊X-tA=I（0st） in Hilbert space with infinite dimension and complex-divisibility was studied.By using operator theory and iterative methods,some necessary conditions and sufficient conditions for the existence of positive solutions to the equation were given.In particular,two sufficient conditions for the positive solutions were given,when A was a normal operator and t=2ms（m was a positive integer）.