Continuous Embeddings, Completions and Complementation in Krein SpacesRadovi Matematički
AbstractLet 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.
Citation InformationBranko Ćurgus and Heinz Langer. "Continuous Embeddings, Completions and Complementation in Krein Spaces" Radovi Matematički Vol. 12 Iss. 1 (2003) p. 37 - 79
Available at: http://works.bepress.com/branko_curgus/27/