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  • 1 Department of Applied Analysis, Eötvös L. University, Pázmány Péter sétány 1/c., Budapest H-1117, Hungary
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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: TT always admits a positive selfadjoint extension. The Friedrichs extension also will be obtained whenever TT is assumed to be densely defined. Selfadjointness of TT 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=TT and at the same time AF=TT∗∗.

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