2011/12/31 by George Eleftherakis, G. K. Eleftherakis, Eleftherakis, G. K.
Mathematics · #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Operator Algebras (math.OA) #math.OA
paper · pdf · doi:10.48550/arxiv.1201.0293
arxiv created 2011/12/31 · openalex publication_date 2011/12/31 · arxiv updated 2012/01/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Recently Blecher and Kashyap have generalized the notion of W* modules over von Neumann algebras to the setting where the operator algebras are σ- weakly closed algebras of operators on a Hilbert space. They call these modules weak* rigged modules. We characterize the weak* rigged modules over nest algebras . We prove that Y is a right weak* rigged module over a nest algebra Alg(M) if and only if there exists a completely isometric normal representation ϕof Y and a nest algebra Alg(N) such that Alg(N)ϕ(Y)Alg(M) ⊂ ϕ(Y) while ϕ(Y) is implemented by a continuous nest homomorphism from M onto N. We describe some properties which are preserved by continuous CSL homomorphisms.