Topological Measure Theory for Double Centralizer Algebras
Topological Measure Theory for Double Centralizer Algebras
The classes of tight, $\tau$-additive, and $\sigma$-additive linear functionals on the double centralizer algebra of a ${C^\ast }$-algebra A are defined. The algebra A is called measure compact if all three classes coincide. Several theorems relating the existence of certain types of approximate identities in A to measure compactness of …