Completion and extension of operators in Kren spaces
Abstract
A generalization of the well-known results of M.G. Kren about the description of selfadjoint contractive extension of a hermitian contraction is obtained. This generalization concerns the situation, where the selfadjoint operator A and extensions A belong to a Kren 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 Kren space. This paper is a natural continuation of S. Hassi's and author's paper [5].
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