Commutative $C^*$-algebras and $\sigma$-normal morphisms

Preprint English OPEN
de Jeu, Marcel;
(2003)
  • Subject: Mathematics - Operator Algebras | 46L05 | Mathematics - Functional Analysis | 46L10

We prove in an elementary fashion that the image of a commutative monotone $\sigma$-complete $C^*$-algebra under a $\sigma$-normal morphism is again monotone $\sigma$-complete and give an application of this result in spectral theory.
  • References (7)

    [1] E. Christensen, Non commutative integration for monotone sequentially closed C∗-algebras, Math. Scand. 31 (1972), 171-190.

    [2] R.V. Kadison and G.K. Pedersen, Equivalence in operator algebras, Math. Scand. 27 (1970), 205-222.

    [3] R.V. Kadison and J.R. Ringrose, Fundamentals of the Theory of Operator Algebras, Volume II, Academic Press, London, 1986.

    [4] G.K. Pedersen, A decomposition theorem for C∗-algebras, Math. Scand. 22 (1968), 266-268.

    [5] G.K. Pedersen, Analysis Now, Springer-Verlag, New York, 1989.

    [6] G.K. Pedersen, C∗-Algebras and their automorphism groups, Academic Press, London, 1979.

    [7] J.D.M. Wright, On minimal σ-completions of C∗-algebras, Bull. London Math. Soc. 6 (1974), 168-174. M.F.E. de Jeu, Mathematical Institute, Leiden University, P.O. Box 9512, 2300 RA Leiden, The Netherlands E-mail address: mdejeu@math.leidenuniv.nl

  • Metrics
Share - Bookmark