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Continuous Embeddings, Completions and Complementation in Krein Spaces
Radovi Matematički
  • Branko Ćurgus, Western Washington University
  • Heinz Langer
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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.
Citation Information
Branko Ćurgus and Heinz Langer. "Continuous Embeddings, Completions and Complementation in Krein Spaces" Radovi Matematički Vol. 12 Iss. 1 (2003) p. 37 - 79
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