Skip to Main Content

Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

What is MCQ? The Mathematical Citation Quotient (MCQ) measures journal impact by looking at citations over a five-year period. Subscribers to MathSciNet may click through for more detailed information.

 

Integral decomposition of functionals on $C^{\ast }$-algebras
HTML articles powered by AMS MathViewer

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
Similar Articles
  • Retrieve articles in Transactions of the American Mathematical Society with MSC: 46L05
  • Retrieve articles in all journals with MSC: 46L05
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