Regular and singular Hermitian operators

Let $A$ be a closed Hermitian operator, let $\mathfrak{H}'$ be the orthogonal complement of the domain of definition of $A$, and let $\mathfrak{R}_\lambda$ be the defect subspace. An operator $A$ is called regular if the orthogonal projection of $\mathfrak{H}'$ on $\mathfrak{R}_\lambda$ is closed. Criteria for regularity are established.