Integral decomposition of functionals on $C^{\ast }$-algebras
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- by Herbert Halpern PDF
- Trans. Amer. Math. Soc. 168 (1972), 371-385 Request permission
Abstract:
The spectrum of the center of the weak closure of a ${C^ \ast }$-algebra with identity on a Hilbert space is mapped into a set of quasi-equivalence classes of representations of the ${C^ \ast }$-algebra so that every positive $\sigma$-weakly continuous functional on the algebra can be written in a central decomposition as an integral over the spectrum of a field of states whose canonical representations are members of the respective quasi-equivalence classes except for a nowhere dense set. Various questions relating to disjointness of classes, factor classes, and uniformly continuous functionals are studied.References
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Additional Information
- © Copyright 1972 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 168 (1972), 371-385
- MSC: Primary 46L05
- DOI: https://doi.org/10.1090/S0002-9947-1972-0296710-7
- MathSciNet review: 0296710