Embeddings, operator ranges, and Dirac operators (Q371610)

The authors continue the study of induced Krein spaces initiated in [\textit{P. Cojuhari} and \textit{A. Gheondea}, J. Oper. Theory 61, No. 2, 347--367 (2009; Zbl 1174.47016)]. The authors introduce the notion of a closely embedded Krein space, which can be considered as a generalization of the concept of closely embedded Hilbert spaces [\textit{P. Cojuhari} and \textit{A. Gheondea}, J. Math. Anal. Appl. 369, No. 1, 60--75 (2010; Zbl 1198.46022)]. Then they present a generalized operator range construction associated to an unbounded selfadjoint operator that yields closed embeddings of Krein spaces. Finally, the results are applied to a general free Dirac operator and the energy space representation is obtained.