NORMAL EXTENSIONS OF LINEAR OPERATORS

Let L-0 be a densely defined minimal linear operator in a Hilbert space H. We prove that if there exists at least one correct extension L-S of L-0 with the property D(L-S) = D(L-S*), then we can describe all correct extensions L with the property D(L) = D(L*). We aL(S)o prove that if L-0 is formally normal and there exists at least one correct normal extension L-N, then we can describe all correct normal extensions L of L-0. As an example, the Cauchy-Riemann operator is considered.