Order theoretical structures in atomic JBW-algebras: disjointness, bands, and centres

IF 0.8 3区数学 Q2 MATHEMATICS

Positivity Pub Date : 2024-01-19 DOI:10.1007/s11117-023-01024-1

引用次数: 0

Abstract

Every atomic JBW-algebra is known to be a direct sum of JBW-algebra factors of type I. Extending Kadison’s anti-lattice theorem, we show that each of these factors is a disjointness free anti-lattice. We characterise disjointness, bands, and disjointness preserving bijections with disjointness preserving inverses in direct sums of disjointness free anti-lattices and, therefore, in atomic JBW-algebras. We show that in unital JB-algebras the algebraic centre and the order theoretical centre are isomorphic. Moreover, the order theoretical centre is a Riesz space of multiplication operators. A survey of JBW-algebra factors of type I is included.

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JBW原子结构中的阶论结构：不相交性、带和中心

摘要众所周知，每个原子 JBW 代数都是 JBW 代数 I 型因子的直和。通过扩展凯迪森反晶格定理，我们证明了这些因子中的每个因子都是无相交反晶格。我们描述了无相交反晶格的直和中的无相交、带和具有无相交保全反的无相交保全双射的特征，因此也描述了原子 JBW-代数中的无相交、带和具有无相交保全反的无相交保全双射的特征。我们证明，在单元 JB-数中，代数中心和阶论中心是同构的。此外，阶论中心是乘法算子的里兹空间。其中还包括对 I 型 JBW-algebra 因子的考察。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Positivity 数学-数学

CiteScore

1.80

自引率

10.00%

发文量

审稿时长

>12 weeks

期刊介绍： The purpose of Positivity is to provide an outlet for high quality original research in all areas of analysis and its applications to other disciplines having a clear and substantive link to the general theme of positivity. Specifically, articles that illustrate applications of positivity to other disciplines - including but not limited to - economics, engineering, life sciences, physics and statistical decision theory are welcome. The scope of Positivity is to publish original papers in all areas of mathematics and its applications that are influenced by positivity concepts.