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On the ranges of bimodule projections

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 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.

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Aristides Katavolos, Vern I. Paulsen. 2003-01-25. On the ranges of bimodule projections. https://doi.org/10.4153/cmb-2005-009-4

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