On the measure of non-compactness of maximal operators

In one of the previous articles of the author it was proved that if B is a convex quasi-density measurable basis and E is a symmetric space on Rn with respect to the Lebesgue measure, then there do not exist non-orthogonal weights w and v for which the maximal operator MB corresponding to B acts compactly from the weight space Ew to the weight space Ev. Here it is given the generalization of this result, in particular, it is estimated from below the measure of non-compactness of the mentioned operators.