Journal of Operator Theory
Volume 63, Issue 2, Spring 2010 pp. 349-362.
Limits of pure functionals of C∗-algebrasAuthors: M.H. Shah
Author institution: Department of Mathematics, Lahore University of Management Sciences (LUMS), 54792-Lahore, Pakistan
Summary: It is shown that, for a C∗-algebra A, every (weak*-) limit of pure functionals is a multiple of a pure functional if and only if every limit of pure states is a multiple of pure states (a condition previously studied by Glimm). On the other hand, it is shown that the set of pure states P(A) being closed does not force the set of pure functionals G(A) to be closed. The conditions ¯G(A) = G(A) and ¯G(A)=G(A)∪{0} are characterised in terms of sums of homogeneous C∗-algebras.
Contents Full-Text PDF