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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, 47L25 show english descriptions unknown classification 46L15
Operator spaces (= matricially normed spaces) [See also 46L07]
46L15 - unknown classification 46L15
47L25 - Operator spaces (= matricially normed spaces) [See also 46L07]
 

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