Normal Conditional Expectations of Finite Index and Sets of Modular Generators
نویسنده
چکیده
Normal conditional expectations E : M → N ⊆ M of finite index on von Neumann algebras M with discrete center are investigated to find an estimate for the minimal number of generators of M as a Hilbert N-module. Analyzing the case of M being finite type I with discrete center we obtain that these von Neumann algebras M are always finitely generated projective N-modules with a minimal generator set consisting of at most [K(E)] modular generators, where [.] denotes the integer part of a real number and K(E) = inf{K : K ·E− idM ≥ 0}. This result contrasts with remarkable examples by P. Jolissaint and S. Popa showing the existence of normal conditional expectations of finite index on certain type II1 von Neumann algebras with center l∞ which are not algebraically of finite index, cf. Y. Watatani. We show that estimates of the minimal number of modular generators by a function of [K(E)] cannot exist for certain type II1 von Neumann algebras with non-trivial center.
منابع مشابه
Normal conditional expectations of finite index and sets of module generators
Normal conditional expectations E : M → N ⊆ M of finite index on von Neumann algebras M with discrete center are investigated to find an estimate for the minimal number of generators of M as a Hilbert N -module. Analyzing the case of M being finite type I with discrete center we obtain that these von Neumann algebras M are always finitely generated projective N -modules with a minimal generator...
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