PUBLICATIONS DE L'INSTITUT MATHÉMATIQUE (BEOGRAD) (N.S.) Vol. 46(60), pp. 141144 (1989) 

A characterization of formally symmetric unbounded operatorsDanko Joci\'cMatematicki fakultet, Beograd, YugoslaviaAbstract: We give necessary and sufficient conditions for an operator in a Hilbert space to be formally symmetric, symmetric or selfadjoint. This generalizes the wellknown fact that a bounded operator $T$ is selfadjoint if and only if $T^\ast T\le(\operatorname{Re}T)^2$. The proof is based on a wellbehaved extension of the corresponding symmetric operator. Classification (MSC2000): 47B25 Full text of the article:
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