Domains of square roots of regularly accretive operators (Q1178768)

Let \(V\), \(H\) be Hilbert spaces such that \(V\hookrightarrow H\) and \(V\) is dense in \(H\). Let \(a: V\times V\to\mathbb{C}\) be a continuous coercive sesquilinear form on \(V\) and denote by \(A\) the operator associated with \(a\) on \(H\). The author finds a new condition (in terms of the decomposition \(a=a_ R+ia_ I\) into two symmetric forms) which implies that \(V=D(A^{1/2})=D(A^{*1/2})\). Application to elliptic operators are given.