TY  - JOUR
ID  - Tarcsay2024
LB  - Tarcsay2024
AU  - Tarcsay, Zsigmond
AU  - Sebestyén, Zoltán
TI  - Reduction of positive self-adjoint extensions
ST  - Reduction of positive self-adjoint extensions
JO  - Opuscula Math.
JA  - Opuscula Math.
JF  - Opuscula Mathematica
PY  - 2024
VL  - 44
IS  - 3
SP  - 425
EP  - 438
DO  - https://doi.org/10.7494/OpMath.2024.44.3.425
UR  - https://doi.org/10.7494/OpMath.2024.44.3.425
AB  - 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.
KW  - positive selfadjoint contractive extension
KW  - nonnegative selfadjoint extension
KW  - Friedrichs and Krein-von Neumann extension
SN  - 1232-9274
ER  -