Bounds for the diamond partial order in B(H)
Bounds for the diamond partial order in B(H)
复制标题
B(H) 中菱形偏序的界限
DOI：
10.1080/03081087.2019.1628912
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发表时间：
2021
影响因子：
1.1
通讯作者：
吉国兴
中科院分区：
文献类型：
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作者：
杨莉莉;吉国兴
设是复Hilbert空间，其维数为上的所有有界线性算子的代数，设是上的菱形阶，即，对于，我们说，如果R（A）<$$> R（B）<$$>，R（A <$）<$$> R（B <$）<$$>和AA <$A=AB <$A。本文考虑了关于菱形偏序的子集的最小上界和最大下界。证明了具有上界的非空子集存在最小上界和最大下界。给出了单调有界网具有上确界和下确界的充要条件。
Letbe a complex Hilbert space with dimandthe algebra of all bounded linear operators on. Letbe the diamond order on, that is, for, we say thatif R(A)¯⊆R(B)¯,R(A∗)¯⊆R(B∗)¯ and AA∗A=AB∗A. We consider the minimal upper bounds and maximal lower bounds of a subset inwith respect to the diamond partial order. It is proved that there exist minimal upper bounds and maximal lower bounds for a nonempty subset with an upper bound. We also give necessary and sufficient conditions for monotone bounded nets to have the supremum as well as infimum.