## Illinois Journal of Mathematics

### The spectral theorem for bimodules in higher rank graph $C\sp *$-algebras

Alan Hopenwasser

#### Abstract

In this note we extend the spectral theorem for bimodules to the higher rank graph $C^*$-algebra context. Under the assumption that the graph is row finite and has no sources, we show that a bimodule over a natural abelian subalgebra is determined by its spectrum iff it is generated by the Cuntz-Krieger partial isometries which it contains iff the bimodule is invariant under the gauge automorphisms. We also show that the natural abelian subalgebra is a masa iff the higher rank graph satisfies an aperiodicity condition.

#### Article information

Source
Illinois J. Math., Volume 49, Number 3 (2005), 993-1000.

Dates
First available in Project Euclid: 13 November 2009

https://projecteuclid.org/euclid.ijm/1258138232

Digital Object Identifier
doi:10.1215/ijm/1258138232

Mathematical Reviews number (MathSciNet)
MR2210272

Zentralblatt MATH identifier
1106.47064

Subjects
Primary: 47L40: Limit algebras, subalgebras of $C^*$-algebras
Secondary: 46L05: General theory of $C^*$-algebras

#### Citation

Hopenwasser, Alan. The spectral theorem for bimodules in higher rank graph $C\sp *$-algebras. Illinois J. Math. 49 (2005), no. 3, 993--1000. doi:10.1215/ijm/1258138232. https://projecteuclid.org/euclid.ijm/1258138232