The alternative Dunford-Pettis property, conjugations and real forms of C*-algebras

• Autores: Leslie J. Bunce , Antonio Miguel Peralta Pereira
• Localización: Journal of the London Mathematical Society, ISSN 0024-6107, Vol. 71, Nº 1, 2005, págs. 161-171
• Idioma: inglés
• DOI: 10.1112/s0024610704005927
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• Resumen

  • 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.