Dilian Yang

Periodicity in Rank 2 Graph Algebras

Kumjian and Pask introduced an aperiodicity condition for higher rank graphs. We present a detailed analysis of when this occurs in certain rank 2 graphs. When the algebra is aperiodic, we give another proof of the simplicity of C(F θ ). The periodic C∗-algebras are characterized, and it is shown that C(F θ ) ≃ C(T)⊗ A where A is a simple C∗-algebra. Department of Pure Mathematics, University of Waterloo, Waterloo, ON N2L 3G1 e-mail: krdavids@uwaterloo.ca Department of Mathematics and Statistics, University of Windsor, Windsor, ON N9B 3P4 e-mail: dyang@uwindsor.ca Received by the editors June 5, 2007. The first author partially supported by an NSERC grant. AMS subject classification: Primary: 47L55; secondary: 47L30, 47L75, 46L05.

A non-self-adjoint Lebesgue decomposition

We study the structure of bounded linear functionals on a class of non-self-adjoint operator algebras that includes the multiplier algebra of every complete Nevanlinna-Pick space, and in particular the multiplier algebra of the Drury-Arveson space. Our main result is a Lebesgue decomposition expressing every linear functional as the sum of an absolutely continuous (i.e. weak-* continuous) linear functional, and a singular linear functional that is far from being absolutely continuous. This is a non-self-adjoint analogue of Takesakis decomposition theorem for linear functionals on von Neumann algebras. We apply our decomposition theorem to prove that the predual of every algebra in this class is (strongly) unique.

The Stability of Jensen’s Equation on Amenable Locally Compact Groups

The stability of Jensen’s equation on amenable locally compact groups is proved in this note.

Boundary quotient C*-algebras of products of odometers

In this paper, we study the boundary quotient C*-algebras associated to products of odometers. One of our main results shows that the boundary quotient C*-algebra of the standard product of

Nonself-adjoint 2-graph algebras

k

The Hopf Structure of Some Dual Operator Algebras

odometers over

Atomic Representations of Rank 2 Graph Algebras

n_i

Characteristic solutions of polynomial-like iterative equations

-letter alphabets (

Remarks on the stability of Drygas' equation and the Pexider-quadratic equation

1\le i\le k

Dilation theory for rank two graph algebras.

) is always nuclear, and that it is a UCT Kirchberg algebra if and only if