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• W2034647210 abstract "Two elements J and K of the complete lattice I(A) of weak*-closed inner ideals in a JBW*-triple A are said to be centrally orthogonal if there exists a weak*-closed ideal I in A such that A2(J) ⊆ A2(I) and A2(K) ⊆ A0(I), and are said to be rigidly collinear when A2(J) ⊆ A1(K) and A2(K) ⊆ A1(J), where, for j equal to 0, 1, or 2, Aj(I), Aj(J), and Aj(K), are the components in the generalized Peirce decomposition of A relative to the weak*-closed inner ideals I, J, and K, respectively. A measure m on I(A) is a mapping from I(A) to C such that, if J and K are either centrally orthogonal or rigidly collinear, thenmJ∨K=mJ+mK.A complex Hilbert space A endowed with a conjugation possesses a triple product and norm with respect to which it forms a JBW*-triple, known as a spin triple. In this paper the structure of the complete lattice I(A) of closed inner ideals in a spin triple A and the measures on it are investigated. It is shown that, if the dimension of A is greater than 5, then there are no non-zero measures on I(A). When the dimension of A is 5, non-zero measures exist and, up to multiplication by a constant, a unique measure exists that is invariant under automorphisms of A. When the dimension of A is 4, then A is triple isomorphic to the W*-algebra of 2 × 2 complex matrices. In this case results of Bunce and Wright are used to show that there is an uncountable number of measures on I(A). The situation when the dimension of A is less than 4 is also described." @default.
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• W2034647210 date "2000-12-01" @default.
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• W2034647210 title "Measures on the Lattice of Closed Inner Ideals in a Spin Triple" @default.
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• W2034647210 doi "https://doi.org/10.1006/jmaa.2000.7059" @default.
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