M-structure in dual Banach spaces |
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Authors: | F. Cunningham Edward G. Effros Nina M. Roy |
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Affiliation: | (1) Bryn Mawr College, University of Pennsylvania, Pennsylvania, USA;(2) Rosemont College, Rosemont, USA |
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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. Supported in part by the National Science Foundation. |
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