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On the Ranges of Bimodule Projections

Published online by Cambridge University Press:  20 November 2018

Aristides Katavolos  and
Vern I. Paulsen
Aristides Katavolos
Affiliation:
Department of Mathematics, University of Athens, Athens, Greece e-mail: akatavol@math.uoa.gr
Vern I. Paulsen
Affiliation:
Department of Mathematics, University of Houston, Houston, TX 77204-3476, U.S.A. e-mail: vern@math.uh.edu
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Abstract

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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 ${{\text{J}}^{*}}$-algebras. We prove that if $P$ is a normal bimodule idempotent and $\left\| P \right\|\,<\,2/\sqrt{3}$ then $P$ is a contraction. We finish with some attempts at extending the symbol calculus to non-normal maps.

Keywords

46L1547L25
Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 48 , Issue 1 , 01 March 2005 , pp. 97 - 111
Copyright
Copyright © Canadian Mathematical Society 2005

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