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Reference: Edwards, CM and G. T. Ruttimann, (2002). The central hull and central kernel in JBW*-triples. Journal of Algebra, 250 (1), 90-114.Citable link to this page:


The central hull and central kernel in JBW*-triples

Abstract: The complete lattice J(A) of weak*-closed inner ideals in a JBW*-triple A has as its centre the complete Boolean algebra LJ(A) of weak*-closed ideals in A. The annihilator L⊥ of the subset L of A consists of elements b of A for which {L b A} is equal to zero, and the kernel Ker(L) of L consists of those elements b in A for which {L b L} is equal to zero. For each element J of J(A), J⊥ also lies in J(A), and A enjoys the generalized Peirce decomposition A=J⊕MJ⊥⊕J1, where J1 is the intersection of the kernels of J and J⊥. To investigate the properties of the weak*-closed subspace J1 of A, which is not, in general, a subtriple, the notions of the central hull c(L) and central kernel k(L) of a subspace L are introduced. These are, respectively, the smallest element of LJ(A) containing L and the largest element of LJ(A) contained in L. For any element J of J(A), the

Author: Edwards, CM - institutionUniversity of Oxford Oxford, MPLS, Mathematical Inst - - - G. T. Ruttimann - - - - Bibliographic Details



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