Abstract
For each state of aC*-algebra its spectrum is defined and shown to coincide with the spectrum of the naturally associated modular operator. For strongly clustering states of asymptotically abelianC*-algebras the spectrum is minimal among the states in the same quasi-equivalence class, hence is a *-isomorphic invariant for the weak closure of the G.N.S.-representation. Furthermore, the non-zero elements in the spectrum of strongly clustering states form a multiplicative group.
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Størmer, E. Spectra of states, and asymptotically abelianC*-algebras. Commun.Math. Phys. 28, 279–294 (1972). https://doi.org/10.1007/BF01645629
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DOI: https://doi.org/10.1007/BF01645629