Direct sums and the Szlenk index |
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| Authors: | Philip AH Brooker |
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| Institution: | Mathematical Sciences Institute, Australian National University, Canberra ACT 0200, Australia |
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| Abstract: | For α an ordinal and 1<p<∞, we determine a necessary and sufficient condition for an ?p-direct sum of operators to have Szlenk index not exceeding ωα. It follows from our results that the Szlenk index of an ?p-direct sum of operators is determined in a natural way by the behaviour of the ε-Szlenk indices of its summands. Our methods give similar results for c0-direct sums. |
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| Keywords: | Szlenk index Asplund operators Direct sums Banach spaces |
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