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

DOI:
https://doi.org/10.1090/S0002-9939-05-08209-2

Published electronically:
December 19, 2005

MathSciNet review:
2215772

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Abstract | References | Similar Articles | Additional Information

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:
https://doi.org/10.1090/S0002-9939-05-08209-2

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.