A bounded linear operator between Banach spaces is called completely continuous if it carries weakly convergent sequences into norm convergent sequences. Isolated is a universal operator for the class of non-completely-continuous operators from L1 into an arbitrary Banach space, namely, the operator from L1 into `∞ defined by T0(f) = Z rnf dμ n≥0 , where rn is the nth Rademacher function. It is...
