The Alternative Dunford–pettis Property, Conjugations and Real Forms of C∗-algebras
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چکیده
Let τ be a conjugation, alias a conjugate linear isometry of order 2, on a complex Banach space X and let Xτ be the real form of X of τ -fixed points. In contrast to the Dunford–Pettis property, the alternative Dunford–Pettis property need not lift from Xτ to X. If X is a C*-algebra it is shown that Xτ has the alternative Dunford–Pettis property if and only if X does and an analogous result is shown when X 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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