Completion and extension of operators in Kre\uın spaces

2016/02/08 by D. Baidiuk, Baidiuk, D.
Mathematics · #47A20 #47A63 #FOS: Mathematics #Functional Analysis (math.FA) #Primary 46C20 #Secondary 47B25 #math.FA #msc:46C20 #msc:47A20 #msc:47A63 #msc:47B25

paper · pdf · doi:10.48550/arxiv.1602.02546

arXiv admin note: text overlap with arXiv:1403.5133

arxiv created 2016/02/08 · arxiv updated 2016/02/09

Abstract

A generalization of the well-known results of M.G. Kre\uın 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 \widetilde A belong to a Kre\uın 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\uın space. This paper is a natural continuation of S. Hassi's and author's paper [5].

Citations

• Completion, extension, factorization, and lifting of operators with a negative index

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