共轭相似及无穷维Hamilton算子的辛自伴性  

Conjugated Similar and Symplectic Self-adjointness of Infinite Dimensional Hamiltonian Operator

作　　者：李琳 阿拉坦仓[1,3] LI Lin1,2, Alatancang1,3(1. School of Mathematical Sciences of Inner Mongolia University, Hohhot 010021, China;2. Department of Physiology of Hetao University, Bayannaoer 015000, China;3. Department of Mathematics of Hohhot Minzu College, Hohhot 010051, Chin)

机构地区：[1]内蒙古大学数学科学学院,内蒙古呼和浩特010021 [2]内蒙古河套学院理学院,内蒙古巴彦淖尔市015000 [3]呼和浩特民族学院数学系,内蒙古呼和浩特010051

出　　处：《数学的实践与认识》2018年第14期298-307,共10页Mathematics in Practice and Theory

基　　金：国家自然科学基金(11761029);河套学除科学技术研究项目(HYZY201TO2)

摘　　要：研究了线性算子的共轭相似，给出共轭相似的线性算子的谱的关系．研究了有界线性算子分别在Banach空间的共轭算子与它在Hilbert空间的共轭算子的关系，研究了无界线性算子分别在Banach空间的共轭算子与在Hilbert空间的共轭算子的关系，并给出了无穷维Hamilton算子辛自伴的等价条件．Conjugated similarity is studied,and a few of properties of the spectrum of conjugated similar linear operators are shown. And, the relationship between the adjoint operator of a bounded line operator in Banach space and its adjoint operator in Hilbert space are studied, and the relationship between the adjoint operator of a unbounded line operator in Banach space and its adjoint operator in Hilbert space are studied. The symplectic self-adjoint conditions of the infinite dimensional Hamilton operator based on similar linear operators are given.

关 键 词：共轭相似 共轭线性算子 无穷维HAMILTON算子 点谱 剩余谱 连续谱 

分 类 号：O177[理学—数学]