秩1幂等元集上的等距满射  

Isometric surjections on rank one idempotents

作　　者：易馨 向彰 YI Xin;XIANG Zhang(School of Mathematical Sciences,Chongqing Normal University,Chongqing 401331,China;School of Mathematics and Statistics,Beijing Institute of Technology,Beijing 102400,China)

机构地区：[1]重庆师范大学数学科学学院,重庆401331 [2]北京理工大学数学与统计学院,北京102400

出　　处：《内江师范学院学报》2023年第4期39-41,共3页Journal of Neijiang Normal University

基　　金：国家自然科学基金资助项目(11871127)。

摘　　要：由于幂等元集结构较投影集更为复杂,且任意秩的幂等元集都是无界集,这对幂等元集合上Wigner定理的推广造成了很多障碍,可以证明:如果φ是秩1幂等元集上的等距映射且存在两个互相正交的秩1投影P、Q,使得φ(P)、φ(Q)也为互相正交的秩1投影,则φ将所有的秩1投影都映成秩1投影.根据经典的Wigner定理可以就φ在秩1投影集上的限制给出具体的刻画.Since the structure of idempotent element sets is more complex than that of projection sets,and idempotent element sets of any rank are unbounded sets,which thus has posed many obstacles to the generalization of Wigner's theorem on idempotent element sets.First,prove the fact that ifφis an isometric mapping on the metaset and there exist two mutually orthogonal rank 1 projections P、Q which makeφ(P)、φ(Q)mutually their own rank 1 orthogonal projections,thenφmakes that all rank 1 projections are mapped into rank 1 projections.According to the classic Wigner theorem,a specific characterizations can be done for the constraints on the set of rank-1 projections.

关 键 词：Wigner定理 等距满射 酉算子 秩1幂等元 

分 类 号：O177.1[理学—数学]