Čebyšëv subspaces of JBW ∗ -triples Jamjoom, Fatmah B. Peralta, Antonio Miguel Siddiqui, Akhlaq A. Tahlawi, Haifa A. Čebyšëv/Chebyshev subspace JBW∗-triples Čebyšëv/Chebyshev subtriple von Neumann algebra Brown-Pedersen quasi-invertibility Spin factor Minimum covering sphere 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. 2015-10-21T09:26:54Z 2015-10-21T09:26:54Z 2015 info:eu-repo/semantics/article Jamjoom, F.B.; et al. Čebyšëv subspaces of JBW ∗ -triples. Journal of Inequalities and Applications, 2015: 288 (2015). [http://hdl.handle.net/10481/38553] 1029-242X http://hdl.handle.net/10481/38553 10.1186/s13660-015-0813-2 eng http://creativecommons.org/licenses/by-nc-nd/3.0/ info:eu-repo/semantics/openAccess Creative Commons Attribution-NonCommercial-NoDerivs 3.0 License Springer Open