Spectra of states,and asymptotically abelianC*-algebras |
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Authors: | Erling Størmer |
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Institution: | (1) University of Oslo, Oslo, Norway |
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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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