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Invariant Inner Ideals in W * ‐algebras
Author(s) -
Edwards C. M.,
Rüttimann G. T.,
Yu. Vasilovsky S.
Publication year - 1995
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19951720108
Subject(s) - mathematics , corollary , invariant (physics) , isomorphism (crystallography) , automorphism , pure mathematics , combinatorics , mathematical physics , crystal structure , chemistry , crystallography
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.