Krein space completion, Complementation in Krein spaces, Operator ranges, Embedding of Krein spaces, Definitizable operators
Let the Krein space (A,[. , . ]A) be continuously embedded in the Krein space (K,[.,.]K ). A unique self-adjoint operator A in K can be associated with(A,[. , . ]A) via the adjoint of the inclusion mapping of A in K. Then (A,[. , . ]A) is a Krein space completion of R(A) equipped with an A-inner product. In general this completion is not unique. If, additionally, the embedding of A in K is t-bounded then the operator A is defnitizable in K and R(A) equipped with the A-inner product has unique Krein space completion. The spectral function of A yields some information about the embedding of A in K. Applications to the complementation theory of deBranges are given.
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Published by: Academy of Arts and Sciences of Bosnia and Herzegovina and Department of Mathematics, University of Sarajevo, Sarajevo, Bosnia and Herzegovina
Link to journal page: http://www.anubih.ba/Journals/_volumes.html
Ćurgus, Branko and Langer, Heinz, "Continuous Embeddings, Completions and Complementation in Krein Spaces" (2003). Mathematics. 72.