The Point Spectrum And Residual Spectrum Of 3×3 Partial Upper Triangular Operator Matrices

According to the denseness and closedness of range of operator T,the point spec-tra and residual spectra of a bounded operator T are split into σp,1(T),σp.2(T)and σr,1(T),σr,2(T).For 3×3 upper triangular operator matrices,the possible point spectra and possible residual spectra, are given and the nec-essary and sufficient condition of σ*,i(MD.E,F)=σ*,i(A)∪σ*.i(B)∪σ*,i(C)(*=p,r；i= 1,2)are described by means of the analysis method and block operator technique.