On the subspaces of JF and JT with non-separable dual |
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Authors: | D Apatsidis V Kanellopoulos |
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Institution: | National Technical University of Athens, Faculty of Applied Sciences, Department of Mathematics, Zografou Campus, 157 80, Athens, Greece |
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Abstract: | It is proved that every subspace of James Tree space (JT) with non-separable dual contains an isomorph of James Tree complemented in JT. This yields that every complemented subspace of JT with non-separable dual is isomorphic to JT. A new JT like space denoted as TF is defined. It is shown that every subspace of James Function space (JF) with non-separable dual contains an isomorph of TF. The later yields that every subspace of JF with non-separable dual contains isomorphs of c0 and ?p for 2?p<∞. The analogues of the above results for bounded linear operators are also proved. |
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Keywords: | Banach spaces with non-separable dual James Tree space James Function space |
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