Completion and extension of operators in Kre\u{\i}n spaces
Functional Analysis
2016-02-09 v1
Abstract
A generalization of the well-known results of M.G. Kre\u{\i}n about the description of selfadjoint contractive extension of a hermitian contraction is obtained. This generalization concerns the situation, where the selfadjoint operator and extensions belong to a Kre\u{\i}n space or a Pontryagin space and their defect operators are allowed to have a fixed number of negative eigenvalues. Also 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 Kre\u{\i}n space. This paper is a natural continuation of S. Hassi's and author's paper [5].
Keywords
Cite
@article{arxiv.1602.02546,
title = {Completion and extension of operators in Kre\u{\i}n spaces},
author = {D. Baidiuk},
journal= {arXiv preprint arXiv:1602.02546},
year = {2016}
}
Comments
arXiv admin note: text overlap with arXiv:1403.5133