W. Stenger's and M.A. Nudelman's results and resolvent formulas involving compressions

Aad Dijksma*, Heinz Langer

*Corresponding author for this work

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    Abstract

    In the first part of this note we give a rather short proof of a generalization of Stenger’s lemma about the compression A to H of a self-adjoint operator A in some Hilbert space H= H⊕ H1. In this situation, S: = A∩ A is a symmetry in H with the canonical self-adjoint extension A and the self-adjoint extension A with exit into H. In the second part we consider relations between the resolvents of A and A like M.G. Krein’s resolvent formula, and corresponding operator models.

    Original languageEnglish
    Pages (from-to)936-949
    Number of pages14
    JournalAdvances in operator theory
    Volume5
    Issue number3
    DOIs
    Publication statusPublished - Jul-2020

    Keywords

    • Hilbert space
    • Dissipative operator
    • Symmetric operator
    • Self-adjoint operator
    • Dilation
    • Compression
    • Extension
    • Generalized resolvent
    • Nevanlinna function
    • Krein's resolvent formula
    • LINEAR RELATIONS

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