Generalized selfadjoinness of differentiation operator on weight Hilbert spases - Ivasiuk, I. Ya. (Methods of Functional Analysis and Topology, 2007)
We consider examples of operators that act in some Hilbert rigging from positive Hilbert space into the negative one. For the first derivative operator we investigate a ``generalized’’ selfadjointness in the sense of weight Hilbert riggings of the spaces L^2([0,1]) and L^2(R). We will show that an example of the operator i ddt in some rigging scales, which is selfadjoint in usual case and not generalized selfadjoint, can not be constructed.