Essential spectra of self-adjoint relations under relatively compact perturbations

Trace class perturbation of closed linear relations

“…We shall remark that this decomposition establishes an important bridge between closed relations and operators. One can apply the properties of the operator T s to study related problems about the closed relation T in some cases (e.g., [13,14,16,19]).…”

“…Enlightened by the idea used in the definitions of compact and finite rank perturbations of closed relations in [2], we shall define the trace class perturbation of closed relations by orthogonal projections (see Definition 3.1). Then we shall study its characterizations, and give out its several equivalent and sufficient characterizations based on the research works in [2,13,14,16,18,19].…”

Perturbation theory for selfadjoint relations

“…Some results of this kind have been obtained for relations being perturbed by relations (see [5,Chap. 7] and [13,14,16,17])…”

“…Thus, taking into account that the main goal of this paper is the detailed analysis of the spectrum of selfadjoint relations under selfadjoint finite rank perturbations, we restrict ourselves to Definition 3. This definition of the essential spectrum is used in [13,14,17], where perturbation theory for relations is treated in a way similar to ours. The results given in this work concerning dissipative relations and the fine-tuning perturbation analysis related to the rank of the perturbation go beyond the results of [13,14,17].…”

“…This definition of the essential spectrum is used in [13,14,17], where perturbation theory for relations is treated in a way similar to ours. The results given in this work concerning dissipative relations and the fine-tuning perturbation analysis related to the rank of the perturbation go beyond the results of [13,14,17].…”