Abstract: | Let X be a Banach space with an unconditional basis such that each operator from X into 2 is 2-absolutely summing. Then X is isomorphic either to co or to 1 or to co1.Translated from Zapiski Nauchnykh Seminarov Leningradskogo Otdeleniya Matematicheskogo Instituta im. V. A. Steklova AN SSSR, Vol. 157, pp. 76–87, 1987.The author is grateful to I. A. Komarchev for a series of useful marks and for the permission to publish the proof of Lemma 1. |