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].
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Translated from Ukrains’kiĭ Matematychnyĭ Visnyk, Vol. 13, No. 4, pp. 452–472 October–December, 2016.
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Baidiuk, D. Completion and extension of operators in Kreĭn spaces. J Math Sci 224, 493–508 (2017). https://doi.org/10.1007/s10958-017-3431-3
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DOI: https://doi.org/10.1007/s10958-017-3431-3