@misc{10481/38553,
year = {2015},
url = {http://hdl.handle.net/10481/38553},
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.},
organization = {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},
keywords = {JBW∗-triples},
keywords = {Čebyšëv/Chebyshev subtriple},
keywords = {von Neumann algebra},
keywords = {Brown-Pedersen quasi-invertibility},
keywords = {Spin factor},
keywords = {Minimum covering sphere},
title = {Čebyšëv subspaces of JBW ∗ -triples},
doi = {10.1186/s13660-015-0813-2},
author = {Jamjoom, Fatmah B. and Peralta, Antonio Miguel and Siddiqui, Akhlaq A. and Tahlawi, Haifa A.},
}