Inner ideals, compact tripotents and Čebyšëv subtriples of JB \(^{*}\) -triples and C
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- 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;