Properties of Pairs of Orthogonal Projections in a Hilbert Space H
Yao Xi-yan · Journal of Southwest China Normal University · 2004
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.