Compact Subsets of the Glimm Space of a C*-algebra. Issue 1 (14th March 2014) - Lazar, Aldo J.
Abstract: If A is a σ -unital C^* -algebra and a is a strictly positive element of A, then for every compact subset K of the complete regularization Glimm (A) of Prim (A) there exists α > 0 such that K {G Glimm(A) \!\!|\!\! \| a + G \| α } . This extends a result of J. Dauns to all σ -unital C^* -algebras. However, there exist a C^* -algebra A and a compact subset of Glimm (A) that is not contained in any set of the form {G Glimm(A) \!\!|\!\! \| a+ G \| α }, a A and α > 0 .