IDEAL STRUCTURE IN FREE SEMIGROUPOID ALGEBRAS FROM DIRECTED GRAPHS

By M. Jury, David W. Kribs. 2003

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A free semigroupoid algebra is the weak operator topol- ogy 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 wot-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 An properties for linear functionals, together with a general Wold Decomposi- tion for n-tuples of partial isometries. A number of our proofs unify proofs for subclasses appearing in the literature.

Subfields: Algebra and Number Theory, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/9a24bb6dc69484915228526aec2ac14d1442a62b

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