Čebyšëv subspaces of JBW ∗ -triples
Metadatos
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Springer Open
Materia
Čebyšëv/Chebyshev subspace JBW∗-triples Čebyšëv/Chebyshev subtriple von Neumann algebra Brown-Pedersen quasi-invertibility Spin factor Minimum covering sphere
Fecha
2015Referencia bibliográfica
Jamjoom, F.B.; et al. Čebyšëv subspaces of JBW ∗ -triples. Journal of Inequalities and Applications, 2015: 288 (2015). [http://hdl.handle.net/10481/38553]
Patrocinador
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.Resumen
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.