Atomic operators can be expressed in the terms of standard operators acting in the spin, orbital and quasispin spaces. Expressions for the tensorial products of such standard operators for dN, fN and gN shells are obtained in terms of some simple operators and a minimal number of operators having nondiagonal matrix elements. These formulas are used to derive the expansion for the Coulomb interaction operator and to investigate some of its properties. The sum rule for the coefficients fk as well as some algebraic relations for the main part of the Coulomb interaction energy are given. The symmetry of these coefficients and of their linear combinations for the ground state of atoms are considered.