(p,Y)-算子Bessel列的广义扰动(英文)

General perturbation of(p,Y)-operator Bessel sequence

运用算子理论,研究了Banach空间中(p,Y)-算子Bessel列的一些广义扰动形式.通过定义新的算子列,证明了已知(p,Y)-算子Bessel列在下三角形式或全矩阵形式的系数矩阵的作用下得到的算子列仍然是(p,Y)-算子Bessel列的充分条件,并得到了通过数列作用在已知(p,Y)-算子Bessel列上构造的一些算子列仍然是(p,Y)-算子Bessel列的充分条件.

By the operator theory, some general perturbations of （p,y）-operator Bessel se- quences in Banach space are mainly studied in this paper. Through defining a new operator se- quence, the sufficient conditions are proved for a lower triangular or a full form of coefficient matrix effecting to a given （p,Y）-operator Bessel sequence, such that the resulted sequence will be still a （p ,Y） -operator Bessel sequence. The sufficient conditions for a sequence of oper- ators compounded by some scalar sequences effecting to a given （p,Y）-operator Bessel sequence to be a （p ,Y） -operator operator Bessel are also obtained.