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- W2000768742 abstract "The kernel Ker(J) and the annihilator J⊥ of a weak*-closed inner ideal J in a JBW*-triple A consist of the sets of elements a in A for which {J a J} and {J a A} are zero, respectively, and J is said to be faithful if, for every non-zero ideal I in A, I ∩ Ker (J) is non-zero. It is shown that every weak*-closed inner ideal J in A has a unique orthogonal decomposition into a faithful weak*-closed inner ideal f(J) and a weak*-closed ideal f (J)⊥ ∩ J of A. The central structure of f ( J) is investigated and used to show that J has zero annihilator if and only if it coincides with the multiplier of f (J). The results are applied to the cases in which J is the Peirce-two or Peirce-zero space A2(v) or A0(v) corresponding to a tripotent v in A, and to the case in which the JBW*-triple A is a von Neumann algebra." @default.
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- W2000768742 date "2003-05-01" @default.
- W2000768742 modified "2023-09-27" @default.
- W2000768742 title "Faithful Inner Ideals in Jbw*-Triples" @default.
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- W2000768742 doi "https://doi.org/10.1007/bf03322740" @default.
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