Document Type
Article
Publication Date
2003
Keywords
Krein space completion, Complementation in Krein spaces, Operator ranges, Embedding of Krein spaces, Definitizable operators
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.
Publication Title
Radovi Matematički
Volume
12
Issue
1
First Page
37
Last Page
79
Required Publisher's Statement
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
Recommended Citation
Ćurgus, Branko and Langer, H., "Continuous Embeddings, Completions and Complementation in Krein Spaces" (2003). Mathematics Faculty Publications. 72.
https://cedar.wwu.edu/math_facpubs/72
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
