Hyperreflexivity of free semigroupoid algebras
Authors:
Frédéric Jaëck and Stephen C. Power
Journal:
Proc. Amer. Math. Soc. 134 (2006), 20272035
MSC (2000):
Primary 47L75
Published electronically:
December 19, 2005
MathSciNet review:
2215772
Fulltext 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 hyperreflexive.
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Additional Information
Frédéric Jaëck
Affiliation:
University of Bordeaux I, LaBAG 351, cours de la Liberation, F33405 Talence, Cedex, France
Email:
jaeck@math.ubordeaux1.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/S0002993905082092
PII:
S 00029939(05)082092
Keywords:
Free semigroupoid,
reflexive algebra,
directed graph,
hyperreflexive
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 HPRNCT200000116 (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.
