Abstract
A nonnegative selfadjoint extension Ãof a nonnegative operator A is called extremal if inf {(Ã)(ϕ) - f),ϕ - f) : ∈ dom A} = 0 for all ϕ ∈ dom Ã.A new construction of all extremal extensions of a nonnegative densely defined operator will be presented.It employs a fixed auxiliary Hilbert space to factorize each extremal extension.Various functional-analytic interpretations of extremal extensions are studied and some new types of characterizations are obtained.In particular,a purely analytic description of extremal extensions is established,based on a class of functions introduced by M.G.Krein and I.E.Ovearenko.
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Arlinskiĭ, Y.M., Hassi, S., Sebestyén, Z., De Snoo, H.S.V. (2001). On the class of extremal extensions of a nonnegative operator. In: Kérchy, L., Gohberg, I., Foias, C.I., Langer, H. (eds) Recent Advances in Operator Theory and Related Topics. Operator Theory: Advances and Applications, vol 127. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8374-0_3
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