幂等算子的左星序

主要研究了Hilbert空间H上全体幂等算子关于左星序的性质, 其中左星序(left-star order)A*≤B定义为A^*A=A^*B且R(A)⊆R(B)。设A和B是幂等算子, 给出了A*≤B的等价条件和算子矩阵形式表示。同时, 当A*≤B时, 讨论了星序的上、下确界A∧B和A∨B的存在性及其表示。

The left-star order for idempotent operators

It is investigated that the characterizations of all idempotent operators on Hilbert space H with respect to the left-star order, which is defined by A^*A=A^*B and R(A)⊆R(B). Let A and B be two idempotent operators, the equivalent condition of A*≤B and the representation of operator matrix form is given. Meanwhile, the existence and representation of A∨B(supremum)and A∧B(infimum)of the star order when A*≤B is discussed.