Remarks on the Istratescu measure of noncompactness

In this paper we give estimations of Istratescu measure of noncompactness $I(X)$ of a set $X\subset l^p(E_1,\dots , E_n)$ in terms of measures $I(X_j) (j = 1,\dots , n)$ of projections $X_j$ of $X$ on $E_j$ . Also a converse problem of finding a set $X$ for which the measure $I(X)$ satisfies the estimations under consideration is considered.