The Boundedness Below of $2×2$ Upper Triangular Linear Relation Matrices

Abstract

In this note, the boundedness below of linear relation matrix), 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 C ∈ BLR(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.