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# On the Ranges of Bimodule Projections

Published:2005-03-01
Printed: Mar 2005
• Aristides Katavolos
• Vern I. Paulsen
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## Abstract

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.
 MSC Classifications: 46L15 - unknown classification 46L1547L25 - Operator spaces (= matricially normed spaces) [See also 46L07]