Ranges of bimodule projections and reflexivity

Details Ranges of bimodule projections and reflexivity Ranges of bimodule projections and reflexivity

2011-08-24

arxiv.org/abs/1108.4829v1

Mathematics

Operator Algebras

Scientific paper

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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