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
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/
@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/}
}