Automorphisms on the Poset of Products of Two Projections  

作　　者：Xin Hui WANG Guo Xing JI 

机构地区：[1]School of Mathematics and Information Science,Shaanxi Normal University

出　　处：《Acta Mathematica Sinica,English Series》2019年第8期1393-1401,共9页数学学报（英文版）

基　　金：Supported by the National Natural Science Foundation of China(Grant No.11771261);the Fundamental Research Funds for the Central Universities(Grant No.GK201801011)

摘　　要：Let H be a complex Hilbert space with dim H ≥ 3 and B(H) the algebra of all bounded linear opera tors on H. Let ≤° be the diamond order on B(H), that is, for A, B ∈B(H), we say that A ≤° B if R(A)■ R(B), R(A^*)■ R(B^*) and AA^*A= AB^*A. Put Λ={PQ : P、Q ∈B(H) are projections}. In this paper, the relationship between Λ and ≤° is revealed and then the form of automorphisms of the poset (Λ,≤°) is given.Let H be a complex Hilbert space with dim H ≥ 3 and B(H) the algebra of all bounded linear operators on H. Let ≤° be the diamond order on B(H), that is, for A, B ∈ B(H), we say that A <° B if ■ and AA~*A = AB~*A.Put Λ = {P Q : P, Q ∈ B(H) are projections}. In this paper, the relationship between Λ and ≤° is revealed and then the form of automorphisms of the poset(Λ, ≤°) is given.

关 键 词：PARTIAL order DIAMOND order product of TWO projections AUTOMORPHISM 

分 类 号：O1[理学—数学]