Abstract
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.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Bibliography
Akemann, C.: The dual space of an operator algebra. Trans. Am. Math. Soc.126 (2), 286–302 (1967).
Dixmier, J.: Les algebres d'operateurs dans l'espace Hilbertien. Paris: Gauthier-Villars 1957.
—— LesC*-algebres et leurs representations. Paris: Gauthier-Villars 1964.
Effros, E.: Order ideals in aC*-algebra and its dual. Duke Math. J.30, 391–412 (1963).
Grothendieck, A.: Sur les applications lineaires faiblement compactes d'espaces du typeC (K). Canad. J. Math.5, 129–173 (1953).
Phillips, R. S.: On linear transformations. Trans. Am. Math. Soc.48, 516–541 (1940).
Sakai, S.: On topological properties ofW*-algebras. Proc. Japan Acad.33, 439–444 (1958).
—— The theory ofW*-algebras. Yale Notes. New Haven, Conn.: Yale University 1962.
Author information
Authors and Affiliations
Rights and permissions
About this article
Cite this article
Akemann, C.A. Sequential convergence in the dual of aW*-algebra. Commun.Math. Phys. 7, 222–224 (1968). https://doi.org/10.1007/BF01645664
Received:
Issue Date:
DOI: https://doi.org/10.1007/BF01645664