Weylness of 2 × 2 operator matrices

Abstract

Let  and  be complex separable infinite-dimensional Hilbert spaces. Given the operators ∈ (), ∈ () and ∈ (, ), we define ∶= [ ] whereis an unknown element. In this paper, a necessary and sufficient condition is given for to be a right Weyl (left Weyl, or Weyl) operator for some ∈ (, ). Moreover, some relevant properties and illustrating examples are also given. K E Y W O R D S

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

“…Recently, 2×2 block operator matrices have attracted attention of many scholars (See, e.g., [5][6][7][8][9][10]). In this work, we consider the linear relations instead of operators and extend some of the existing results.…”