M-structure in dual Banach spaces |
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| Authors: | F Cunningham Edward G Effros Nina M Roy |
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| Institution: | (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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| Keywords: | |
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