(untitled) (Journal of Mathematical Study, 2024)
In this note, the boundedness below of linear relation matrix M_C=(smallmatrix A & C 0 & B smallmatrix )LR(HK) is considered, where ACLR(H), BCLR(K), CBLR(K,H), H,K are separable Hilbert spaces. By suitable space decompositions, a necessary and sufficient condition for diagonal relations A,B is given so that M_C is bounded below for some CBLR(K,H). Besides, the characterization of σ_ap(M_C) and σ_su(M_C) are obtained, and the relationship between σ_ap(M_0) and σ_ap(M_C) is further presented.