Geodesic
A Characterization of Formally Symmetric Unbounded Operators
Publications de l'Institut Mathématique, _N_S_46 (1989) no. 60, p. 141 Cet article a éte moissonné depuis la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

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We give necessary and sufficient conditions for an operator in a Hilbert space to be formally symmetric, symmetric or self-adjoint. This generalizes the well-known fact that a bounded operator $T$ is self-adjoint if and only if $T^\ast T\le(\operatorname{Re}T)^2$. The proof is based on a well-behaved extension of the corresponding symmetric operator.
Classification : 47B25 
@article{PIM_1989_N_S_46_60_a19,
     author = {Danko Joci\'c},
     title = {A {Characterization} of {Formally} {Symmetric} {Unbounded} {Operators}},
     journal = {Publications de l'Institut Math\'ematique},
     pages = {141 },
     year = {1989},
     volume = {_N_S_46},
     number = {60},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PIM_1989_N_S_46_60_a19/}
}
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Danko Jocić. A Characterization of Formally Symmetric Unbounded Operators. Publications de l'Institut Mathématique, _N_S_46 (1989) no. 60, p. 141 . http://geodesic.mathdoc.fr/item/PIM_1989_N_S_46_60_a19/