Ranges of bimodule projections and reflexivity |
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Authors: | G.K. Eleftherakis I.G. Todorov |
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Affiliation: | 1. Department of Mathematics, University of Athens, Panepistimioupolis 157 84, Athens, Greece;2. Department of Pure Mathematics, Queen?s University Belfast, Belfast BT7 1NN, United Kingdom |
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Abstract: | We develop a general framework for reflexivity in dual Banach spaces, motivated by the question of when the weak? closed linear span of two reflexive masa-bimodules is automatically reflexive. We establish an affirmative answer to this question in a number of cases by examining two new classes of masa-bimodules, defined in terms of ranges of masa-bimodule projections. We give a number of corollaries of our results concerning operator and spectral synthesis, and show that the classes of masa-bimodules we study are operator synthetic if and only if they are strong operator Ditkin. |
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