Record number :

1549334

Title of article :

Extensions of Pure States and Projections of Norm One

Author/Authors :

Archbold، نويسنده , , R.J.، نويسنده ,

Issue Information :

روزنامه با شماره پیاپی سال 1999

Pages :

20

From page :

24

To page :

43

Abstract :

We show that the extension property for pure states of a C*-subalgebra B of a C*-algebra A leads to the existence of a projection of norm one R: A→B in the case where B is liminal with Hausdorff primitive ideal space. Furthermore, R is given by a “Dixmier process” in which the averaging is effected by a group of unitary elements in the centre of the multiplier algebra M(B). These results generalize earlier work of J. Anderson and the author for the case when B is a masa of A. Various applications are given in the context of inductive limit algebras such as AF algebras and, more generally, Kumjianʹs ultraliminary C*-algebras.

Keywords :

C*-algebras , Pure state , unique extension , projection of norm one , ultraliminary , AF algebra

Journal title :

Journal of Functional Analysis

Serial Year :

1999

Link To Document :