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Invariant subspaces for operators in a general II1-factor

Uffe HaagerupHanne Schultz — 2009

Publications Mathématiques de l'IHÉS

Let ℳ be a von Neumann factor of type II1 with a normalized trace τ. In 1983 L. G. Brown showed that to every operator T∈ℳ one can in a natural way associate a spectral distribution measure μ T (now called the Brown measure of T), which is a probability measure in ℂ with support in the spectrum σ(T) of T. In this paper it is shown that for every T∈ℳ and every Borel set B in ℂ, there is a unique closed T-invariant subspace 𝒦 = 𝒦 T ( B ) affiliated with ℳ, such that the Brown measure of T | 𝒦 is concentrated on B...

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