arXiv math/03012982003-01math.OAmath.FA

On the ranges of bimodule projections

Aristides Katavolos, Vern I. Paulsen

备注：: Please refer to the journal for the final version
发表信息：: Canad. Math. Bull. Vol. 48(1), 2005, 97-111
DOI：: 10.4153/CMB-2005-009-4

英文摘要：

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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