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We develop a symbol calculus for normal bimodule maps over a masa that is the natural analogue of the Schur product theory. Using this calculus we are able to easily give a complete description of the ranges of contractive normal bimodule idempotents that avoids the theory of J*-algebras. We prove that if $P$ is a normal bimodule idempotent and $|P| < 2/sqrt{3}$ then $P$ is a contraction. We finish with some attempts at extending the symbol calculus to non-normal maps.
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
In deformation-rigidity theory it is often important to know whether certain bimodules are weakly contained in the coarse bimodule. Consider a bimodule $H$ over the group algebra $mathbb{C}[Gamma]$, with $Gamma$ a discrete group. The starting point o
We study containment and uniqueness problems concerning matrix convex sets. First, to what extent is a matrix convex set determined by its first level? Our results in this direction quantify the disparity between two product operations, namely the pr
Let $A$ be a unital AF-algebra whose Murray-von Neumann order of projections is a lattice. For any two equivalence classes $[p]$ and $[q]$ of projections we write $[p]sqsubseteq [q]$ iff for every primitive ideal $mathfrak p$ of $A$ either $p/mathfra
We consider two-variable model spaces associated to rational inner functions $Theta$ on the bidisk, which always possess canonical $z_2$-invariant subspaces $mathcal{S}_2.$ A particularly interesting compression of the shift is the compression of mul