On the Ranges of Bimodule Projections

http://dx.doi.org/10.4153/CMB-2005-009-4
Canad. Math. Bull. 48(2005), 97-111

  Published:2005-03-01
 Printed: Mar 2005

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 easily able to 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.