Mathematics – Operator Algebras
Scientific paper
2003-11-12
Trans. Amer. Math. Soc., 357 (2005), 3739-3755.
Mathematics
Operator Algebras
22 pages, Trans. Amer. Math. Soc., to appear
Scientific paper
Based on a Wold decomposition for families of partial isometries and projections of Cuntz-Krieger-Toeplitz-type, we extend several fundamental theorems from the case of single vertex graphs to the general case of countable directed graphs with no sinks. We prove a Szego-type factorization theorem for CKT families, which leads to information on the structure of the unit ball in free semigroupoid algebras, and show that joint similarity implies joint unitary equivalence for such families. For each graph we prove a generalization of von Neumann's inequality which applies to row contractions of operators on Hilbert space which are related to the graph in a natural way. This yields a functional calculus determined by quiver algebras and free semigroupoid algebras. We establish a generalization of Coburn's theorem for the C*-algebra of a CKT family, and prove a universality theorem for C*-algebras generated by these families. In both cases, the C*-algebras generated by quiver algebras play the universal role.
Katsoulis Elias
Kribs David W.
No associations
LandOfFree
Applications of the Wold decomposition to the study of row contractions associated with directed graphs does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Applications of the Wold decomposition to the study of row contractions associated with directed graphs, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Applications of the Wold decomposition to the study of row contractions associated with directed graphs will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-337433