On the Ranges of Bimodule Projections

Abstract

AbstractWe 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 then P is a contraction. We finish with some attempts at extending the symbol calculus to non-normal maps.