缺项算子矩阵的二阶代数(Ⅰ)(英文)

Quadric Completion of Operator Partial Matrices (Ⅰ)

英文关键词:operator matrix  completion.

中文摘要:

      对于任意给定的二阶多项式ｐ（ｔ）；本文获得希尔伯特空间上形如（?）的缺项算子矩阵具有一个补Ｔ使得ｐ（Ｔ）＝０成立的充分必要条件以及使得ｐ（Ｔ）＝０且ｐ（Ｔ）的范数不大于事先给定常数的充分必要条件．进而还求出所有可能的二阶代数补，特别地，对有限维情形给出简洁的表示。

英文摘要:

      For a given quadric polynomial p(t), the necessary and sufficient conditions are obtained for operator partial matrices of the form (?) to be completed to an operator T such that p(T) = 0. Moreover, all such possible completions, if exist, are presented parametrically.