A new upgrade theorem for relative biexactness under mixing conditions yields a classification of biexactness for graph products of finite-dimensional von Neumann algebras, extending prior results.
and Ozawa, Narutaka , TITLE =
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Strict comparison holds in the uniform Roe algebra of any countable discrete amenable group, with an additional strong AH result for the crossed product by the universal minimal set.
Minimal sufficient Jordan algebras characterize sufficiency for positive trace-preserving maps on quantum states, with Neyman-Pearson tests generating them and equality in data-processing inequalities implying Petz recovery.
Constructs first non-locally trivial W*-bundle with fixed II1 factor fibres via a uniform spectral gap obstruction for bundles with factorial fibres.
Von Neumann algebras of Artin groups encode the number of connected components of their defining graphs except possibly for free-group-factor cases; a similar result holds for Coxeter groups absent relative hyperbolicity.
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Relative biexactness and mixing in von Neumann algebras
A new upgrade theorem for relative biexactness under mixing conditions yields a classification of biexactness for graph products of finite-dimensional von Neumann algebras, extending prior results.
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Strict comparison holds in the uniform Roe algebra of a discrete amenable group
Strict comparison holds in the uniform Roe algebra of any countable discrete amenable group, with an additional strong AH result for the crossed product by the universal minimal set.
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A non-locally trivial $\mathrm{W}^*$-bundle with fixed factorial fibres
Constructs first non-locally trivial W*-bundle with fixed II1 factor fibres via a uniform spectral gap obstruction for bundles with factorial fibres.