Spectra of principal graphs

Kodiyalam, Vijay ; Sunder, V. S. (2001) Spectra of principal graphs International Journal of Mathematics, 12 (2). pp. 203-210. ISSN 0129-167X

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Official URL: http://www.worldscinet.com/ijm/12/1202/S0129167X01...

Related URL: http://dx.doi.org/10.1142/S0129167X01000691


We show that if the adjacency matrices of the two principal graphs of a finite index subfactor are regarded as (necessarily bounded, self-adjoint) operators on the ℓ2 spaces over their vertex sets, then their spectral measures, when restricted to the complement of {0}, are mutually absolutely continuous. In particular, for a finite-depth subfactor, the two matrices have the same sets of non-zero eigenvalues.

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