Closability Property of Operator Algebras Generated by Normal Operators and Operators of Class $C_0$
Dr. Hao-Wei HuangIndiana University 下午 3:00–3:50 鴻經館 107 室Abstract:
An operator algebra A acting on a Hilbert space is said to have the closability property if every densely de‾ned linear transformation commuting with A is closable. In this talk, I will review the results obtained in the ‾eld and other related properties. Then I will give necessary and su±cient conditions for a normal operator N such that the von Neumann algebra generated by N has the closability property. I will also characterize the operator T of class C0 for which the algebra H1(T) = fu(T) : u 2 H1g has the closability property which is shown to be equivalent to two signi‾cant properties in the class C0.