Abstract

A result previously known only for certain ordered Banach spaces is generalized to arbitrary real Banach spaces. Let ℒ be the Banach algebra of operators generated by theL-projections of a real Banach spaceU, and let ℳ (U * be the bounded operators on the dual spaceU * with adjoint in ℒ(U **. Then the adjoint operation maps ℒ (U) onto ℳ (U *). In particular, anyM-projection ofU * is weak* continuous.

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