Extensions of positive symmetric operators and Krein's uniqueness criteria

2022/09/01 by Sebestyén, Zoltán, Tarcsay, Zsigmond
#47A20 Secondary: 47B25 #FOS: Mathematics #Functional Analysis (math.FA) #Primary: 47A57

paper · doi:10.48550/arxiv.2209.00318

Abstract

We revise Krein's extension theory of positive symmetric operators. Our approach using factorization through an auxiliary Hilbert space has several advantages: it can be applied to non-densely defined transformations and it works in both real and complex spaces. As an application of the results and the construction we consider positive self-adjoint extensions of the modulus square operator T^*T of a densely defined linear transformation T and bounded self-adjoint extensions of a symmetric operator. Krein's results on the uniqueness of positive (respectively, norm preserving) self-adjoint extensions are also revised.

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