Ideal Structure in Free Semigroupoid Algebras from Directed Graphs

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A free semigroupoid algebra is the weak operator topology closed algebra generated by the left regular representation of a directed graph. We establish lattice isomorphisms between ideals and invariant subspaces, and this leads to a complete description of the weak operator topology closed ideal structure for these algebras. We prove a distance formula to ideals, and this gives an appropriate version of the Caratheodory interpolation theorem. Our analysis rests on an investigation of predual properties, specifically the $A_n$ properties for linear functionals, together with a general Wold Decomposition for $n$-tuples of partial isometries. A number of our proofs unify proofs for subclasses appearing in the literature.
32 pages, J. Operator Theory, to appear

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Operator Algebras, 47L55, 47L75

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http://salesiana.dossiersoluciones.com/handle/123456789/102018

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0309397
 http://arxiv.org/abs/math/0309397
 J. Operator Theory, 53 (2005), 273-302.

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arXiv