On the ranges of bimodule projections

Details On the ranges of bimodule projections On the ranges of bimodule projections

2003-01-25

arxiv.org/abs/math/0301298v3

Canad. Math. Bull. Vol. 48(1), 2005, 97-111

Mathematics

Operator Algebras

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Scientific paper

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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