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http://dx.doi.org/10.4134/BKMS.2010.47.4.743

THE ALTERNATIVE DUNFORD-PETTIS PROPERTY IN SUBSPACES OF OPERATOR IDEALS  

Moshtaghioun, S. Mohammad (DEPARTMENT OF MATHEMATICS UNIVERSITY OF YAZD)
Publication Information
Bulletin of the Korean Mathematical Society / v.47, no.4, 2010 , pp. 743-750 More about this Journal
Abstract
For several Banach spaces X and Y and operator ideal $\cal{U}$, if $\cal{U}$(X, Y) denotes the component of operator ideal $\cal{U}$; according to Freedman's definitions, it is shown that a necessary and sufficient condition for a closed subspace $\cal{M}$ of $\cal{U}$(X, Y) to have the alternative Dunford-Pettis property is that all evaluation operators $\phi_x\;:\;\cal{M}\;{\rightarrow}\;Y$ and $\psi_{y^*}\;:\;\cal{M}\;{\rightarrow}\;X^*$ are DP1 operators, where $\phi_x(T)\;=\;Tx$ and $\psi_{y^*}(T)\;=\;T^*y^*$ for $x\;{\in}\;X$, $y^*\;{\in}\;Y^*$ and $T\;{\in}\;\cal{M}$.
Keywords
Dunford-Pettis property; Schauder decomposition; compact operator; operator ideal;
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