Hyper-reflexivity of free semigroupoid algebras

Details Hyper-reflexivity of free semigroupoid algebras Hyper-reflexivity of free semigroupoid algebras

2003-11-12

arxiv.org/abs/math/0311201v2

Mathematics

Operator Algebras

Corrected version, to appear in the Proceedings of the A.M.S

Scientific paper

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 L_G is generated by a family of partial isometries, and initial projections, acting on a generalized Fock space spawned from the directed graph G. We show that if the graph is finite then the algebra L_G is hyper-reflexive.

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