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Hyper-reflexivity of free semigroupoid algebras

Authors: Frédéric Jaëck and Stephen C. Power
Journal: Proc. Amer. Math. Soc. 134 (2006), 2027-2035
MSC (2000): Primary 47L75
Published electronically: December 19, 2005
MathSciNet review: 2215772
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Abstract: As a generalization of the free semigroup algebras considered by Davidson and Pitts, and others, the second author and D.W. Kribs initiated a study of reflexive algebras associated with directed graphs. A free semigroupoid algebra $ \mathcal{L}_G$ is generated by a family of partial isometries, and initial projections, which act on a generalized Fock space spawned by the directed graph $ G$. We show that if the graph is finite, then $ \mathcal{L}_G$ is hyper-reflexive.

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Additional Information

Frédéric Jaëck
Affiliation: University of Bordeaux I, LaBAG 351, cours de la Liberation, F-33405 Talence, Cedex, France

Stephen C. Power
Affiliation: Department of Mathematics and Statistics, Lancaster University, Lancaster, Lancashire LA1, England

Keywords: Free semigroupoid, reflexive algebra, directed graph, hyper-reflexive
Received by editor(s): February 10, 2005
Published electronically: December 19, 2005
Additional Notes: This work is part of the research program of the network “Analysis and Operators" supported by the European Community’s Potential Program under HPRN-CT-2000-00116 (Analysis and operators).
Communicated by: David R. Larson
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.