TENSOR PRODUCTS OF JACOBSON RADICALS IN NEST ALGEBRAS

• 作 者: 董浙
• 机 构: Department of Mathematics, Institute of Mathematics
• 出 处: 数学年刊B辑
• 发表日期: 2004年期
• 关键词: Jacobson radical Tensor product Nest algebra

This paper studies the tensor product RN w RM of Jacobson radicals in nest algebras,and obtains that RN w RM = {T ∈B(H1 H2): T ( N M) N_ M_ , N ∈ N, M ∈ M};and based on the characterization of rank-one operators in RN w RM, it is proved that ifN, M are non-trivial then RN w RM = RwN M if and only if N, M are continuous.