Hilbert空间H上正交射影对的性质

Properties of Pairs of Orthogonal Projections in a Hilbert Space H

研究了Hilbert空间H上正则射影对的性质和结构,证明了两个正交射影P1,P2是可交换的(i.e.,P1P2= P2P1)两个等价刻画:(a)对某些p,q≥2及i,j=1,2,P(p;i)=P(q;j)成立;(b)对每一个p,q≥2及i,j=1,2,P(p;i) =P(q;j)成立.

In the paper, properties and structure of regular pairs of orthogonal projections are discussed. The aim is to find a useful tool for proving a main result in the note. Moreover, two equivalent cheracterizations that two orthogonal projections P_1,P_2 is commutative are proved : (a) for some p,q≥2 and i,j=1,2, P_((p;i))=P_((q;j)) holds; (b) for every p,q≥2 and i,j=1,2, P_((p;i))=P_((q;j)) holds.