Completion and extension of operators in Kreĭn spaces
- Authors: Baidiuk D.1
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Affiliations:
- Department of Mathematics and Statistics, University of Vaasa
- Issue: Vol 224, No 4 (2017)
- Pages: 493-508
- Section: Article
- URL: https://journals.rcsi.science/1072-3374/article/view/239632
- DOI: https://doi.org/10.1007/s10958-017-3431-3
- ID: 239632
Cite item
Abstract
A generalization of the well-known results of M.G. Kreĭn on the description of the self-adjoint contractive extension of a Hermitian contraction is obtained. This generalization concerns the situation where the self-adjoint operator A and extensions e à belong to a Kreĭn space or a Pontryagin space, and their defect operators are allowed to have a fixed number of negative eigenvalues. A result of Yu. L. Shmul’yan on completions of nonnegative block operators is generalized for block operators with a fixed number of negative eigenvalues in a Kreĭn space.
This paper is a natural continuation of S. Hassi’s and author’s recent paper [7].
About the authors
Dmytro Baidiuk
Department of Mathematics and Statistics, University of Vaasa
Author for correspondence.
Email: dbaidiuk@uwasa.fi
Finland, Vaasa