Communications in Mathematical Physics

, Volume 7, Issue 3, pp 222–224 | Cite as

Sequential convergence in the dual of aW*-algebra

  • Charles A. Akemann


The present paper is the result of the author's attempt to extend Theorem 9 of [5] to the case of a non-abelianW*-algebra. In [5]Grothendieck proves that weak and weak* convergence are equivalent for sequences in the dual space of an abelianW*-algebra. Theorem 4 of the present paper is only a partial result in that direction, but it is presented here because of its possible worth as a technical tool.


Neural Network Statistical Physic Complex System Nonlinear Dynamics Quantum Computing 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. 1.
    Akemann, C.: The dual space of an operator algebra. Trans. Am. Math. Soc.126 (2), 286–302 (1967).Google Scholar
  2. 2.
    Dixmier, J.: Les algebres d'operateurs dans l'espace Hilbertien. Paris: Gauthier-Villars 1957.Google Scholar
  3. 3.
    —— LesC*-algebres et leurs representations. Paris: Gauthier-Villars 1964.Google Scholar
  4. 4.
    Effros, E.: Order ideals in aC*-algebra and its dual. Duke Math. J.30, 391–412 (1963).Google Scholar
  5. 5.
    Grothendieck, A.: Sur les applications lineaires faiblement compactes d'espaces du typeC (K). Canad. J. Math.5, 129–173 (1953).Google Scholar
  6. 6.
    Phillips, R. S.: On linear transformations. Trans. Am. Math. Soc.48, 516–541 (1940).Google Scholar
  7. 7.
    Sakai, S.: On topological properties ofW*-algebras. Proc. Japan Acad.33, 439–444 (1958).Google Scholar
  8. 8.
    —— The theory ofW*-algebras. Yale Notes. New Haven, Conn.: Yale University 1962.Google Scholar

Copyright information

© Springer-Verlag 1968

Authors and Affiliations

  • Charles A. Akemann
    • 1
  1. 1.Dept. of MathematicsUniv. of PennsylvaniaUSA

Personalised recommendations