On the Ranges of Bimodule Projections

[摘要] We develop a symbol calculus for normal bimodule maps over a masathat is the natural analogue of the Schur product theory. Usingthis calculus we are easily able to give a complete description ofthe ranges of contractive normal bimodule idempotents that avoidsthe theory of J*-algebras. We prove that if $P$ is a normalbimodule idempotent and $|P| < 2/sqrt{3}$ then $P$ is acontraction. We finish with some attempts at extending the symbolcalculus to non-normal maps.

[学科分类] 数学（综合）

[关键词] Weak compactness;projectional resolutions;Markushevich bases;Eberlein compacts;Vav sák spaces