On free entropy dimension of finite von Neumann algebras
β Scribed by L. Ge; J. Shen
- Publisher
- Springer
- Year
- 2002
- Tongue
- English
- Weight
- 241 KB
- Volume
- 12
- Category
- Article
- ISSN
- 1016-443X
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π SIMILAR VOLUMES
We show the analogue for the entropy of automorphisms of finite von Neumann algebras of the classical formula H(T )=H( i=0 T &i P | i=1 T &i P), where T is a measure preserving transformation of a probability space, and P is a generator.
We modify slightly Voiculescu's definition of approximation entropy of automorphisms of finite von Neumann algebras and compare it with the entropy of Connes and Sto% rmer. For this the notion of a generator is relevant, as its existence implies that the entropies coincide. Special emphasis is put o
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.