算子偏序的刻画及性质

Characters and Properties of Partial Orders of Operators

中文关键词:  算子分块矩阵  算子偏序  特殊算子.

英文关键词:operator block matrice  operator partial order  special operator

中文摘要:

      本文定义了Hilbert空间上两个算子间的四种关系:星序、左星序、右星序及减序, 使用了算子分块矩阵的方法, 给出了两个算子具有上述四种关系之一时它们几何结构的刻画, 证明了这四种关系是真正的偏序关系, 进一步研究了它们之间的关系和性质.

英文摘要:

      We define four types of relations of two operators on Hilbert space: star, left-star, right-star and minus orders, respectively. Using the method of operator block matrices, we give the geometric characterizations of these orders. We prove that these orders are realy partial orders. Furthermore, we give relationships among these operator partial orders and their properties.