Examples of discrete operators with a pure point spectrum of finite multiplicity
The following results are given in the present paper: Result 1. Given a certain diagonal matrix \(D\) and a perturbation \(P\) on \(\ell^2(\mathbb{Z}^m)\), then there exist a diagonal matrix \(\widehat D\) and an invertible matrix \(V\) such that \(V^{-1}(P+\widehat D)V= D\). Result 2. Given a certain diagonal matrix \(D\) and a discrete operator \(Q\) on \(\ell^2(\mathbb{Z}^m)^N\), where \(N\) is an \(n\)-integer, then there exist a diagonal matrix \(\widehat D\) and an invertible matrix \(V\) such that \(V^{-1}(Q+\widehat D)V= D\). The proofs of these results are based on some useful lemmas.
scientific article; zbMATH DE number 1246310