2

There's a theorem about a unique (up to unitary equivalence) decomposition of non-denereate (multiplicity-free in this case) representations of separable GCR $C^*$-algebras (see e.g. Dixmier, 8.6.5) into direct integral of irreducible ones.

Is there such decomposition in the non-separable GCR case (as hinted here)? Most of the references I found focus on a separable case. Perhaps there are some weaker generalizations for some special (non-separable) cases?

plllnt
  • 350
  • And a broader question which I decided non to include in the main question: are irreducible representations are not as useful in a non-separable case? Or can we still use them to tell something about any representation? – plllnt Sep 07 '22 at 14:34
  • what is a GCR C*-algebra? – Just dropped in Sep 07 '22 at 19:59
  • @alepopoulo110 it means that image of any irreducible representation contains compact operators (https://math.stackexchange.com/questions/537120/in-how-far-are-ccr-and-gcr-c-algebras-interesting?) – plllnt Sep 07 '22 at 20:40
  • @alepopoulo110 I should also mention that Dixmier calls them postliminal – plllnt Sep 07 '22 at 20:45

0 Answers0