You Long YANG,Xiao Guang GAO
Hopenwasser A.[1] guessed that the operator set of the CSL algebra satisfying Ringrose condition just is its Jacobson radical; Davidson K. R.[2] proved that this conjecture is true on the width-two CSL. In this paper, the structure of Jacobson radical on the width-two CSL is described clearly, and an. aproach for analyzing the CSLs radical is provided. Let be a width-two CSL generated by nests M and N in a separable Hilbert space, and W = M∩ N. We prove an important relationship , where is the Jacobson radical of alga and Rw, are the Jacobson radical and the stronger radical of nest W respectively. Also, it has been derivedt that the sufficient and necessary conditions for are M ≠ K and M≠K⊥.