Illinois Journal of Mathematics

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

Alan Hopenwasser

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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

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

First available in Project Euclid: 13 November 2009

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Digital Object Identifier

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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


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.

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