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. S. , Hilbert Space Operators , Birkhäuser (Boston, 2003). MR 2004f :47001 Kubrusly C. S. Hilbert Space Operators
Abstract
T ∗ T is selfadjoint if T is a densely defined closed Hilbert space operator. This result of von Neumann can be generalized for not necessarily closed operators: T∗T always admits a positive selfadjoint extension. The Friedrichs extension also will be obtained whenever T∗T is assumed to be densely defined. Selfadjointness of T∗T will be investigated. Densely defined positive operators and their Friedrichs extension A and AF, respectively, will be described by showing the existence of a closable operator T such that A=T∗T and at the same time AF=T∗T∗∗.
space operators , Quaestiones Math. , 41 ( 2018 ), 585 - 600 . [12] Patrício , P. , The Moore-Penrose inverse of a companion
