On the essential spectrum of matrix operators (Q1922336)

Let \(L=\left[\begin{smallmatrix} A & B\\ C & D\end{smallmatrix}\right]\) be an unbounded matrix operator acting on a Banach space. It is shown in the present paper that, under some suitable assumption, \(L\) is closable if and only if \(S(\mu)\) is and the essential spectrum of \(L\) is the union of that of \(A\) and \(S(\mu)\).