矩阵代数上保持投影组联合谱的映射  

Mapping Preserving the Joint Spectrum of Projections in Matrix Algebras

作　　者：陶唐洪 TAO Tanghong(School of Mathematical Science,Chongqing Normal University,Chongqing 401331)

机构地区：[1]重庆师范大学数学科学学院,重庆忠县401331

出　　处：《绵阳师范学院学报》2024年第5期1-6,共6页Journal of Mianyang Teachers＇ College

基　　金：重庆市科委自然科学基金项目(cstc2020jcyj-msxmX0723)。

摘　　要：设A=A1⊕A2,其中A_(1)■Mm(C),A_(2)■Mn(C)(2≤m,n(≠m)),P(A)是A中所有(正交)投影构成的集合.如果φ是P(A)到自身的满射且保持任意两个投影的联合谱,则φ=φ_(1)⊕φ_(2),其中φ_(i)是P(A_(i))到自身保持两个投影联合谱的满射.进一步,如果m与n中有一个等于2,则相应的φi是任意满足φ_(i)(0)=0,φ_(i)(I)=I的双射.否则,φ_(i)都是由复数域C的环自同构诱导的映射.In this paper,suppose that A=A_(1)⊕A_(2) where A_(1)■Mm(C)and A_(2)■Mn(C)with m,n≥2 and m≠n,P(A)is the set of projections in A.Ifφ:P(A)→P(A)is a surjective mapping which preserves the joint spectrum of any two projections in A,then there are two surjective mappings φ_(i):P(Ai)→P(A_(i))which preserve the joint spectrum of any two projections in Ai and such that φ=φ_(1)⊕φ_(2).Furthermore,if n>m=2,then φ_(1) is any bijection on P(A_(1))∖{0,I_(1)}.Otherwise,the mapping φ_(i)(i=1,2)is induced by a ring automorphism of the field C.

关 键 词：投影 联合谱 矩阵代数 环自同构 

分 类 号：O177.1[理学—数学]