Hilbert空间中一类非线性算子方程正算子解的刻画

Characterization of positive operator solutions for a class of nonlinear operator equation in Hilbert space

在无限维Hilbert空间上,利用算子论的相关知识,研究非线性算子方程X^(s)-A&(*)X^(-t)A=Q的正算子解问题。给出了算子方程X^(s)-A&(*)X^(-t)A=Q有正算子解的一些必要条件和充分条件,并研究了方程有正算子解时方程中各算子之间的代数结构和关系。

The positive operator solution of nonlinear operator equation X^(s)-A&(*)X^(-t)A=Q is studied on infinite dimension Hilbert space.Using the related knowledge of operator theory,some necessary and sufficient conditions for the existence of positive operator solutions for X^(s)-A&(*)X^(-t)A=Q is established.Moreover,the algebraic structures and relations of operators in equations with positive operator solutions are studied.