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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
Posted:
December 19, 2005
MathSciNet review:
2215772
Full-text PDF Free Access
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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  is generated by a family of partial isometries, and initial projections, which act on a generalized Fock space spawned by the directed graph  . We show that if the graph is finite, then  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
Email:
jaeck@math.u-bordeaux1.fr
Stephen C. Power
Affiliation:
Department of Mathematics and Statistics, Lancaster University, Lancaster, Lancashire LA1, England
Email:
s.power@lancaster.ac.uk
DOI:
http://dx.doi.org/10.1090/S0002-9939-05-08209-2
PII:
S 0002-9939(05)08209-2
Keywords:
Free semigroupoid,
reflexive algebra,
directed graph,
hyper-reflexive
Received by editor(s):
February 10, 2005
Posted:
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 after
28 years from publication.
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