Čebyšëv subspaces of JBW↿/sup>-triples

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• 作者：Fatmah B Jamjoom ; Antonio M Peralta…
• 关键词：Čebyšëv/Chebyshev subspace ; JBW∗ ; triples ; Čebyšëv/Chebyshev subtriple ; von Neumann algebra ; Brown ; Pedersen quasi ; invertibility ; spin factor ; minimum covering sphere
• 刊名：Journal of Inequalities and Applications
• 出版年：2015
• 出版时间：December 2015
• 年：2015
• 卷：2015
• 期：1
• 全文大小：1,657 KB
• 刊物主题：Analysis; Applications of Mathematics; Mathematics, general;
• 出版者：Springer International Publishing
• ISSN：1029-242X

文摘

We describe the one-dimensional Čebyšëv subspaces of a JBW∗-triple M by showing that for a non-zero element x in M, \(\mathbb{C}x\) is a Čebyšëv subspace of M if and only if x is a Brown-Pedersen quasi-invertible element in M. We study the Čebyšëv JBW∗-subtriples of a JBW∗-triple M. We prove that for each non-zero Čebyšëv JBW∗-subtriple N of M, exactly one of the following statements holds: (a) N is a rank-one JBW∗-triple with \(\dim(N)\geq2\) (i.e., a complex Hilbert space regarded as a type 1 Cartan factor). Moreover, N may be a closed subspace of arbitrary dimension and M may have arbitrary rank;