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Please use this identifier to cite or link to this item: http://hdl.handle.net/10481/38553

Title: Čebyšëv subspaces of JBW ∗ -triples
Authors: Jamjoom, Fatmah B.
Peralta, Antonio Miguel
Siddiqui, Akhlaq A.
Tahlawi, Haifa A.
Issue Date: 2015
Abstract: We describe the one-dimensional Čebyšëv subspaces of a JBW ∗ -triple M by showing that for a non-zero element x in M, Cx 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)≥2 (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; (b) N=Ce, where e is a complete tripotent in M; (c) N and M have rank two, but N may have arbitrary dimension ≥2; (d) N has rank greater than or equal to three, and N=M. We also provide new examples of Čebyšëv subspaces of classic Banach spaces in connection with ternary rings of operators.
Sponsorship: The authors extend their appreciation to the Deanship of Scientific Research at King Saud University for funding this work through research group No. RG-1435-020. The second author also is partially supported by the Spanish Ministry of Economy and Competitiveness project No. MTM2014-58984-P.
Publisher: Springer Open
Keywords: Čebyšëv/Chebyshev subspace
JBW∗-triples
Čebyšëv/Chebyshev subtriple
von Neumann algebra
Brown-Pedersen quasi-invertibility
Spin factor
Minimum covering sphere
URI: http://hdl.handle.net/10481/38553
ISSN: 1029-242X
Rights : Creative Commons Attribution-NonCommercial-NoDerivs 3.0 License
Citation: Jamjoom, F.B.; et al. Čebyšëv subspaces of JBW ∗ -triples. Journal of Inequalities and Applications, 2015: 288 (2015). [http://hdl.handle.net/10481/38553]
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