Commutative C^*algebras and sequentially normal morphisms
Abstract
We show that the image of a commutative monotone sequentially complete C^*algebra, under a sequentially normal morphism, is again a monotone sequentially complete C^*algebra, and also a monotone sequentially closed C^*subalgebra. As a consequence, the image of an algebra of this type, under a sequentially normal representation in a separable Hilbert space, is strongly closed. In the case of a unital representation of C(X) in a separable Hilbert space, where X is a compact Hausdorff space, this implies that the von Neumann algebra generated by the image of C(X) is the image of the Baire functions on X under the extension of the representation to the bounded Borel functions.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 November 2003
 arXiv:
 arXiv:math/0311107
 Bibcode:
 2003math.....11107D
 Keywords:

 Operator Algebras;
 Functional Analysis;
 46L05;
 46L10
 EPrint:
 LaTeX, 4 pages, 1 figure