Ranges of bimodule projections and reflexivity

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.