1型次对角代数的超代数与非交换解析Toeplitz代数

Super-algebras and noncommutative analytic Toeplitz algebras of type 1 subdiagonal algebras

设M是σ-有限von Neunann代数,A是M中关于忠实正规条件期望Φ的1型次对角代数.本文研究基于A的超代数与非交换Hp空间上的非交换解析Toeplitz代数.本文还证明M中任一个包含A的σ-弱闭子代数也是1型次对角代数,同时,在非交换H^(p)(1<p<∞)空间上的非交换右(左)解析Toeplitz代数是遗传自反代数.

Let M be aσ-nite von Neumann algebra and A a type 1 subdiagonal algebra with respect to a faithful normal conditional expectation Φ.We consider super-algebras and noncommutative analytic Toeplitz algebras on the noncommutative H^(p) spaces associated with A.We show that aσ-weakly closed subalgebra containing A in M is also a type 1 subdiagonal algebra.Moreover,the right(respectively left)noncommutative analytic Toeplitz algebra on the noncommutative H^(p)(1<p<∞)space is a hereditary re exive algebra.