Applications of Operator Space Theory to Nest Algebra Bimodules

作者：Eleftherakis G K^*

来源：Integral Equations and Operator Theory, 2012, 72(4): 577-595.

DOI：10.1007/s00020-012-1961-0

• Nest algebras
• Morita equivalence
• Hilbert modules

Recently, Blecher and Kashyap have generalized the notion of W*-modules over von Neumann algebras to the setting where the operator algebras are sigma-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 Phi of Y and a nest algebra Alg(N) such that Alg(N)Phi(Y)Alg(M) subset of Phi(Y) while Phi(Y) is implemented by a continuous nest homomorphism from M onto N. We describe some properties which are preserved by continuous CSL homomorphisms.

• 出版日期2012-4