| Abstract: | We characterize those positive (not necessarily densely defined) operators whose Krein–von Neumann extension, the smallest among all positive selfadjoint extensions, has closed range. In addition, we construct their Moore–Penrose pseudoinverse by employing factorization via an auxiliary Hilbert space. Other extremal extensions, in particular the Friedrichs extension, are also investigated from this point of view. As an application, new characterizations of essentially selfadjoint positive operators are presented. |
