具纯离散谱的u-标算子  

u-SCALAR OPERATORS WITH PURELY DISCRETE SPECTRUM

作　　者：孙万贵[1] 王春峰[1] 吴开谡[2] 

机构地区：[1]天津大学系统工程研究所 [2]中国原子能科学研究院,北京102413

出　　处：《系统科学与数学》2003年第4期501-507,共7页Journal of Systems Science and Mathematical Sciences

摘　　要：本文研究一类具纯离散谱的非自伴算子,证明了该类算子在弱拓扑意义下可以特征展开的充分必要条件是该类算子是u-标的(u-scalar),又等价于该类算子拟仿射相似于自伴算子.并给出例子,说明其在弱拓扑意义下可以特征展开,但不属于经典的标型谱算子(Spectral operator of scalar type).A class of non-selfadjoint operators is discussed in this paper. The necessary and sufficient conditions for an operator with purely discrete spectrum to be u-scalar are given. And some examples are given to illustrate the difference between a u-scalar operator and a spectral operator of scalar type.

关 键 词：U-标算子 非自伴算子 弱拓扑 充分必要条件 纯离散谱 

分 类 号：O177[理学—数学]