论文标题
成对的投影和通勤异构体
Pairs of projections and commuting isometries
论文作者
论文摘要
It is known that the non-zero part of compact defect operators of Berger-Coburn-Lebow pairs (BCL pairs in short) of isometries are diagonal operators of the form \[ \begin{bmatrix} I_1 & & & \\ & D & & \\ & & - I_2 & \\ & & & - D \\ \end{bmatrix}, \] where $ i_1 $和$ i_2 $是身份操作员，$ d $是一个正面的染色对角线操作员。我们讨论了从上述类型的对角线运算符中构建不可还原的BCL对的问题。这个问题的答案有时是肯定的，有时是负面的。这也回答了He，Qin和Yang提出的问题的一部分。我们对BCL对的显式结构产生了一对通勤等法对的具体实例。
It is known that the non-zero part of compact defect operators of Berger-Coburn-Lebow pairs (BCL pairs in short) of isometries are diagonal operators of the form \[ \begin{bmatrix} I_1 & & & \\ & D & & \\ & & - I_2 & \\ & & & - D \\ \end{bmatrix}, \] where $I_1$ and $I_2$ are the identity operators and $D$ is a positive contractive diagonal operator. We discuss the question of constructing an irreducible BCL pair from a diagonal operator of the above type. The answer to this question is sometimes in the affirmative and sometimes in the negative. This also answers a part of the question raised by He, Qin, and Yang. Our explicit constructions of BCL pairs yield concrete examples of pairs of commuting isometries.
