Leslie J. Bunce , Antonio Miguel Peralta Pereira
Let be a conjugation, alias a conjugate linear isometry of order 2, on a complex Banach space and let be the real form of of -fixed points. In contrast to the Dunford-Pettis property, the alternative Dunford-Pettis property need not lift from to . If is a C*-algebra it is shown that has the alternative Dunford-Pettis property if and only if does and an analogous result is shown when is the dual space of a C*-algebra. One consequence is that both Dunford-Pettis properties coincide on all real forms of C*-algebras.
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