In this paper we define and study certain von Neumann algebra invariants associated to the Dirac operator acting on L 2 spinors on the universal covering space of a compact, Riemannian spin manifold. We first study a Novikov Shubin type invariant, which is a conformal invariant but which is not inde
Operator valued weights in von Neumann algebras, II
โ Scribed by Uffe Haagerup
- Publisher
- Elsevier Science
- Year
- 1979
- Tongue
- English
- Weight
- 1022 KB
- Volume
- 33
- Category
- Article
- ISSN
- 0022-1236
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๐ SIMILAR VOLUMES
It is proved that any power-bounded operator of class C 1, } in a finite von Neumann algebra is conjugate to a unitary. This solves a conjecture stated by I. Kovacs in 1970. An important ingredient of the proof is the study of completely positive projections on some operator space.
We associate to any contraction T (and, more generally, to any operator T of class C \ ) in a von Neumann algebra M an operator kernel K : (T) (|:| <1) which allows us to define various kinds of functional calculis for T. When M is finite, we use this kernel to give a short proof of the Fuglede Kadi
Contents. 0. Introduction. 1. The bundle algebra A. 2. Representation of the bundle algebra A. 3. The dual action and the trace. 4. The local characteristic square extended unitary group and modular automorphism group. 5. Conclusions.