On the Facial Structure of the Unit Balls in a JBW∗‐Triple and its Predual
On the Facial Structure of the Unit Balls in a JBW∗‐Triple and its Predual
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JBW*-三元组中单位球的面结构及其预演
DOI：
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发表时间：
1988
期刊：
影响因子：
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通讯作者：
G. Rüttimann
中科院分区：
文献类型：
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作者：
C. Edwards;G. Rüttimann
证明了JBW*-三元21的三次幂等元的集合是一个完备格，序同构于单位球中的范数闭面格&“！反序同构于SI中单位球Ulj的弱*闭面格。其结果是，W*-代数中的偏等距集具有其自然序，并且再加上一个最大元素，构成一个完整的格，其单位球的每个非空弱*闭面形如M+(1 MM*)21(1-？)！对于某些唯一的部分等距M。
The set of tripotents in a JBW*-triple 21 with its natural ordering and with a largest element adjoined is shown to be a complete lattice, order isomorphic to the lattice of norm closed faces in the unit ball &„! of the predual 21* of 21 and anti-order isomorphic to the lattice of weak* closed faces of the unit ball Ulj in SI. As a consequence, the set of partial isometries in a W*-algebra with its natural ordering and again with a largest element adjoined forms a complete lattice and every non-empty weak* closed face of its unit ball is of the form M + (1 MM*) 21(1 -«*«) ! for some unique partial isometry M.