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