One-sided projections on C*-algebras
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We obtain several equivalent characterizations of linear maps on a C*-algebra A which are given by left multiplication by a fixed orthogonal projection in (resp. fixed element in) A or its multiplier algebra. These results are connected to the 'complete one-sided M-ideals' in operator spaces recently introduced by Blecher, Effros, and Zarikian. Part of the proof makes use of a technique to "solve" multi-linear equations in von Neumann algebras. This technique is also applied to show that preduals of von Neumann algebras have no nontrivial complete one-sided M-ideals. We also show that the intersection of two complete one-sided M-summands need not be a one-sided M-summand.