Completion and extension of operators in Krein spaces

摘要

A generalization of the well-known results of M.G. Krein 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 A belong to a Krem 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 Krein space. This paper is a natural continuation of S. Hassi's and author's recent paper [7].