Let be a locally compact Hausdorff space. An algebra of continuous trace over is a -algebra with dual space , such that Fell’s condition holds: for each , there is such that is a rank-one projection for each in a neighbourhood of . This holds if and only if the set of all for which the map is finite and continuous on is dense in . A Fell algebra is a -algebra which satisfies Fell’s condition but is not necessarily Hausdorff.
A continuous trace -algebra is, to some extent, an operator algebraic counterpart to the theory of Azumaya algebras. Dixmier-Douady class has been designed originally to give invariant of such operator algebras.
Last revised on July 10, 2024 at 15:20:31. See the history of this page for a list of all contributions to it.