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- W2924838326 abstract "We construct Markov semi-groups $mathcal{T}$ and associated BMO-spaces on a finite von Neumann algebra $(mathcal{M}, tau)$ and obtain results for perturbations of commutators and non-commutative Lipschitz estimates. In particular, we prove that for any $A in mathcal{M}$ self-adjoint and $f: mathbb{R} rightarrow mathbb{R}$ Lipschitz there is a Markov semi-group $mathcal{T}$ such that for $x in mathcal{M}$, [ Vert [f(A), x] Vert_{{rm BMO}(mathcal{M}, mathcal{T})} leq c_{abs} Vert f' Vert_infty Vert [A, x] Vert_infty. ] We obtain an analogue of this result for more general von Neumann valued-functions $f: mathbb{R}^n rightarrow mathcal{N}$ by imposing Hormander-Mikhlin type assumptions on $f$. In establishing these result we show that Markov dilations of Markov semi-groups have certain automatic continuity properties. We also show that Markov semi-groups of double operator integrals admit (standard and reversed) Markov dilations." @default.
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- W2924838326 date "2019-03-26" @default.
- W2924838326 modified "2023-09-27" @default.
- W2924838326 title "BMO-estimates for non-commutative vector valued Lipschitz functions" @default.
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