【摘要】 算子方程是算子论中的一个热点问题,近年来得到很大的发展.利用算子论知识和构造迭代序列的方法,研究算子方程X^s+A*X^-tA=Q的正算子解的问题,给出了算子方程X^s+A*X^-tA=Q正算子解存在的一些必要条件和充分条件,并研究了方程中各算子的范数、谱半径之间的关系,确定了解的范围.更多还原

【Abstract】 In this paper,by using the operator theory and the iterative sequence,the positive operator solutions to the operator equation X^s+ A*X^-tA = Q are studied. The necessary conditions and sufficient conditions for the existence of positive operator solutions to the equation are derived respectively. Also,the relations of operators A,Q and X in the form of norm and spectral radius are discussed when the equation has positive solutions. And the range of the solutions is determined.更多还原