The p-approximations and inverse problems of expansion and contraction of n-fermion operators

The orthogonal projectors from the space $\text{L}$(n) of n-fermion operators onto its sub-spaces $\text{L}$_p(n) consisting of p-reducible elements of $\text{L}$(n>), as well as those from $\text{L}$(n) onto $\text{L}$_p(n)?$\text{L}$_p?1(n) are constructed. Using the above projectors the inverse problems of contraction and expansion are solved.