投影算子组的联合谱  

The joint spectrum of a tuple of projections

作　　者：吴文明 蒋叶聪 阮颖彬[2] 钱文华 Wenming Wu;Yecong Jiang;Yingbin Ruan;Wenhua Qian

机构地区：[1]重庆师范大学数学科学学院,重庆401331 [2]福建师范大学数信学院,福州350117

出　　处：《中国科学：数学》2021年第5期711-722,共12页Scientia Sinica：Mathematica

基　　金：国家自然科学基金(批准号:11871127,11801050,11671133和11971463);重庆市科委项目(批准号:cstc2019jcyj-msxmX0256);重庆市教委科学技术研究(批准号:KJQN2018000538)资助项目。

摘　　要：本文研究Hilbert空间H上投影算子组的联合谱.首先通过计算给出正则投影对的联合谱,进而给出一般的投影算子对的联合谱.本文还对两个投影算子的和与差的可逆性给出一些等价刻画.特别地,当P和Q为正则投影对时,本文通过计算算子组[I, P, Q]的联合谱来给出σ(P+Q)和σ(P-Q)的具体刻画.反过来,本文证明两类具有特定形式的复数集分别是Hilbert空间上正则投影对的和与差的谱.本文也给出一般的投影算子对的和与差的谱.最后,本文计算特定条件下的3个投影算子组[P, Q, R]的联合谱.We study the joint spectrum of projections in a Hilbert space, and calculate the joint spectrum of a pair of projections. In particular, by calculating the joint spectrum for a tuple [I, P, Q] in which I is the identity and P, Q is a regular pair of projections, we get specific characterizations of the spectrums of P + Q and P-Q,respectively. Conversely, we prove that two closed subsets of C in particular forms are respectively the spectrums of the sum and the difference of a regular pair of projections. We also calculate the joint spectrum of a 3-tuple of projections [P, Q, R] for P, Q and R satisfying some specific conditions.

关 键 词：投影算子组 联合谱 正则投影对 

分 类 号：O177[理学—数学]