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Weak*–closed Jordan ideals of nest algebras
Author(s) -
Oliveira Lina
Publication year - 2003
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.200310008
Subject(s) - converse , mathematics , nest algebra , ideal (ethics) , pure mathematics , class (philosophy) , nest (protein structural motif) , set (abstract data type) , jordan algebra , algebra over a field , algebra representation , non associative algebra , computer science , geometry , philosophy , physics , epistemology , nuclear magnetic resonance , artificial intelligence , programming language
Nest algebras provide examples of partial Jordan *–triples. If A is a nest algebra and A s = A ∩ A*, where A * is the set of the adjoints of the operators lying in A , then ( A , A s ) forms a partial Jordan *–triple. Any weak*–closed ideal in the nest algebra A is also an ideal in the partial Jordan *–triple ( A , A s ). An analysis of the ideal structure of ( A , A s ) shows that, for a large class of nest algebras, the converse is also true.