Regular C*-valued weights

Abstract

We introduce the notion of a C*-valued weight between two C*-algebras as a generalization of an ordinary weight on a C*-algebra and as a C*-version of operator valued weights on von Neumann algebras. Also, some form of lower semi-continuity will be discussed together with an extension to the multiplier algebra. A strong but useful condition for C*-valued weights, the so-called regularity, is introduced. At the same time, we propose a construction procedure for such regular C*-valued weights. This construction procedure will be used to define the tensor product of regular C*-valued weights.

LaTeX, 58 pages

References in corpus (1)

• KMS-weights on C*-algebras

Cited by in corpus (6)

• Weight theory for C*-algebraic quantum groups
• Non-compact quantum groups arising from Heisenberg type Lie bialgebras
• Hecke algebras of semidirect products and the finite part of the Connes-Marcolli C*-algebra
• Integrable and proper actions on C*-algebras, and square-integrable representations of groups
• Locally compact quantum groupoid
• Induced corepresentations of locally compact quantum groups