On determining the domain of the adjoint operator
  A theorem that is of aid in computing the domain of the adjoint operator is provided. It may serve e.g. as a criterion for selfadjointness of a symmetric operator, for normality of a formally normal operator or for $H$--selfadjointness of an $H$--symmetric operator. Differential operators and operators given by an infinite matrix are considered as examples. 
Michal Wojtylak
math.FA math.SP