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Journal of Operator Theory

Volume 63, Issue 2, Spring 2010  pp. 349-362.

Limits of pure functionals of C-algebras

Authors 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.


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