Inner ideals, compact tripotents and Čebyšëv subtriples of JB \(^{*}\) -triples and C 详细信息    查看全文

• 作者：Fatmah B. Jamjoom ; Antonio M. Peralta…
• 关键词：Čebyšëv/Chebyshev subspace ; JB\(^*\) ; triples ; Čebyšëv/Chebyshev subtriple ; von Neumann algebra ; C\(^*\) ; algebra ; Brown ; Pedersen quasi ; invertibility ; spin factor
• 刊名：Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas
• 出版年：2017
• 出版时间：January 2017
• 年：2017
• 卷：111
• 期：1
• 页码：129-138
• 全文大小：413KB
• 刊物类别：Mathematics and Statistics
• 刊物主题：Mathematics, general; Applications of Mathematics; Theoretical, Mathematical and Computational Physics;
• 出版者：Springer Milan
• ISSN：1579-1505
• 卷排序：111

文摘

The aim of this note is to study Čebyšëv JB\(^*\)-subtriples of general JB\(^*\)-triples. It is established that if F is a non-zero Čebyšëv JB\(^*\)-subtriple of a JB\(^*\)-triple E, then exactly one of the following statements holds:(a)F is a rank one JBW\(^*\)-triple with dim \((F)\ge 2\) (i.e. a complex Hilbert space regarded as a type 1 Cartan factor). Moreover, F may be a closed subspace of arbitrary dimension and E may have arbitrary rank;