Weak*–closed Jordan ideals of nest algebras | Zendy

Oliveira Lina | Zendy

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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.

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