Suppose that L(r, D) is a pseudo-differential operator with the symbol L(z,.), that is, (L(z, D)](x) = (2r)'_"J where F is the Fourier transform from the Schwartz class S onto S. The paper considers the equality of the minimal and maximal realizations of L(z, D) in the L 2 (R")-space. Employing the symbolic calculus of Weyl sufficient criteria for the equality are proved. Also some (counter) examples for the mentioned equality are presented.