@Article{Tarcsay2024,
author = "Tarcsay, Zsigmond and Sebestyén, Zoltán",
title = "Reduction of positive self-adjoint extensions",
journal = "Opuscula Math.",
year = "2024",
volume = "44",
number = "3",
pages = "425--438",
doi = "https://doi.org/10.7494/OpMath.2024.44.3.425",
url = "https://doi.org/10.7494/OpMath.2024.44.3.425",
abstract = "We revise Krein's extension theory of semi-bounded Hermitian operators by reducing the problem to finding all positive and contractive extensions of the \"resolvent operator\" \((I+T)^{-1}\) of \(T\). Our treatment is somewhat simpler and more natural than Krein's original method which was based on the Krein transform \((I-T)(I+T)^{-1}\). Apart from being positive and symmetric, we do not impose any further constraints on the operator \(T\): neither its closedness nor the density of its domain is assumed. Moreover, our arguments remain valid in both real or complex Hilbert spaces.",
keywords = "positive selfadjoint contractive extension, nonnegative selfadjoint extension, Friedrichs and Krein-von Neumann extension",
issn = "1232-9274"
}