Article
Continuous Embeddings, Completions and Complementation in Krein Spaces
Radovi Matematički
Document Type
Article
Publication Date
1-1-2003
Keywords
- Krein space completion,
- Complementation in Krein spaces,
- Operator ranges,
- Embedding of Krein spaces,
- Definitizable operators
Disciplines
Abstract
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.
Subjects - Topical (LCSH)
Kreĭn spaces; Definite integrals
Genre/Form
articles
Type
Text
Rights
Copying of this document in whole or in part is allowable only for scholarly purposes. It is understood, however, that any copying or publication of this document for commercial purposes, or for financial gain, shall not be allowed without the author’s written permission.
Language
English
Format
application/pdf
Citation Information
Branko Ćurgus and H. 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/