Weak*–closed Jordan ideals of nest algebras

✍ Scribed by Lina Oliveira

• Publisher: John Wiley and Sons
• Year: 2003
• Tongue: English
• Weight: 204 KB
• Volume: 248-249
• Category: Article
• ISSN: 0025-584X
• DOI: 10.1002/mana.200310008

✦ Synopsis

Abstract

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.