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Invariant Inner Ideals in W*-algebras

✍ Scribed by C. M. Edwards; G. T. Rüttimann; S. Yu. Vasilovsky

Publisher
John Wiley and Sons
Year
1995
Tongue
English
Weight
713 KB
Volume
172
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

Let H(B,α) be the JBW^*^‐algebra of elements of a continuous W^*^‐algebra B invariant under the ^*^‐anti‐automorphism α of B of order two. Then the mapping I → I ∩ H(B, α) is an order isomorphism from the complete lattice of α‐invariant weak^*^ closed inner ideals in B onto the complete lattice of weak^*^ closed inner ideals in H(B, α), every one of which is of the form eH(B, α) α(e) for some unique projection e in B with α‐invariant central support. A corollary of this result completely characterizes the weak^*^ closed inner ideals in any continuous JBW^*^‐triple.

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