Geodesic
A Characterization of Formally Symmetric Unbounded Operators
Publications de l'Institut Mathématique, _N_S_46 (1989) no. 60, p. 141 .

Voir la notice de l'article provenant de la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

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 },
     publisher = {mathdoc},
     volume = {_N_S_46},
     number = {60},
     year = {1989},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PIM_1989_N_S_46_60_a19/}
}
TY  - JOUR
AU  - Danko Jocić
TI  - A Characterization of Formally Symmetric Unbounded Operators
JO  - Publications de l'Institut Mathématique
PY  - 1989
SP  - 141 
VL  - _N_S_46
IS  - 60
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/PIM_1989_N_S_46_60_a19/
LA  - en
ID  - PIM_1989_N_S_46_60_a19
ER  - 
%0 Journal Article
%A Danko Jocić
%T A Characterization of Formally Symmetric Unbounded Operators
%J Publications de l'Institut Mathématique
%D 1989
%P 141 
%V _N_S_46
%N 60
%I mathdoc
%U http://geodesic.mathdoc.fr/item/PIM_1989_N_S_46_60_a19/
%G en
%F PIM_1989_N_S_46_60_a19
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/