Hyper-reflexivity of free semigroupoid algebras

Jaëck, Frédéric; Power, Stephen

doi:10.1090/S0002-9939-05-08209-2

Hyper-reflexivity of free semigroupoid algebras
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by Frédéric Jaëck and Stephen C. Power PDF

Proc. Amer. Math. Soc. 134 (2006), 2027-2035 Request permission

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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