Hilbert空间上可交换算子集合的超循环性

Hypercyclicity of the Set of Commuting Operators on Hilbert Space

Hilbert空间上具有超循环性的算子对于研究空间性质有重要的作用.在本文中,讨论了Hilbert空间上可交换算子集合的超循环问题,给出了一个可交换算子集合具有公共的稠的超循环子空间的充分条件.从而为进一步研究Hilbert空间上算子的超循环性提供了条件.

Hilbert space with hypercyclic operators plays an important role in studing the properties of the space. In this paper, we study hypercyclicity of the set of commuting operators on Hilbert space, give a sufficient condition for the set of commuting operators on Hilbert space sharing a dense hypercyclic subspace. And then we provide the conditions for continuing to study the hypercyclicty of operators on Hilbert space.