Some types of identities of subspaces $M_0^{(m,k)}(F)$, $M_1^{(m,k)}(F)$ of matrix superalgebra $M^{(m,k)}(F)$

Some types of polynomials of free associative algebra $F\{Z\}$ have been introduced and investigated. The conditions under which these polynomials are the identities of subspaces $M_0^{(m, k)}(F)$, $M_1^{(m,k)}(F)$ of superalgebra $M^{(m, k)}(F)$ have been found.