Amenable absorption in amalgamated free product von Neumann algebras

Cyril Houdayer; R\'emi Boutonnet

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Amenable absorption in amalgamated free product von Neumann algebras

Rémi Boutonnet, Cyril Houdayer

Operator Algebras · Submitted 2 Jun 2016

abstract compiled · 2026-09-23 · no language-model review

The authors' main claim Our main result states that under natural analytic assumptions, any amenable subalgebra of $M$ that has a large intersection with $M_1$ is actually contained in $M_1$.

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We investigate the position of amenable subalgebras in arbitrary amalgamated free product von Neumann algebras $M = M_1 \ast_B M_2$. Our main result states that under natural analytic assumptions, any amenable subalgebra of $M$ that has a large intersection with $M_1$ is actually contained in $M_1$. The proof does not rely on Popa's asymptotic orthogonality property but on the study of non normal conditional expectations.

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#	sentence	role	the authors' own work	states the main conclusion	strength
s0	We investigate the position of amenable subalgebras in arbitrary amalgamated free product von Neumann algebras $M = M_1 \ast_B M_2$.	contribution 0.65	0.86	0.03	asserted 0.61
s1	Our main result states that under natural analytic assumptions, any amenable subalgebra of $M$ that has a large intersection with $M_1$ is actually contained in $M_1$.	result 1.00	0.95	0.98	asserted 1.00
s2	The proof does not rely on Popa's asymptotic orthogonality property but on the study of non normal conditional expectations.	method 0.95	0.90	0.03	asserted 1.00

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Original abstract

We investigate the position of amenable subalgebras in arbitrary amalgamated free product von Neumann algebras $M = M_1 \ast_B M_2$. Our main result states that under natural analytic assumptions, any amenable subalgebra of $M$ that has a large intersection with $M_1$ is actually contained in $M_1$. The proof does not rely on Popa's asymptotic orthogonality property but on the study of non normal conditional expectations.

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5 arXiv papers cite this in 19 sentences

Each citing sentence is taken from the citing paper's LaTeX source and typed by Pith's classifier. A label appears at probability 0.8 or more (0.95 for support), a contest at 0.7 or more; the quoted words are the citing authors'. How each label was checked · JSON

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Uses its method or tool 4 papers

Instead, we use the notion of relative amenability via the existence of non normal conditional expectations as in [ref] and we apply the main result of [ref] regarding amenable absorption in arbitrary AFP von Neumann algebras.

Factoriality, Connes' type III invariants and fullness of amalgamated free product von Neumann algebras · Factoriality of AFP von Neumann algebras · 0.95
We prove the following maximal amenability property by combining Popa's asymptotic orthogonality [ref] with the method of [ref] .

Thin II_1 factors with no Cartan subalgebras · Maximal amenability · 0.99
In the type $$ case, we use instead the result obtained in Theorem [ref], and we exploit the recent generalization of Popa's intertwining theory to arbitrary von Neumann algebras (see [ref] ) to prove the unique McDuff decomposition.

Fullness and Connes' $\boldsymbol{\tau}$ invariant of type III tensor product factors · Statement of the main results · 0.93

Cites it as background 1 paper

We refer the reader to [ref] for further information regarding Popa's intertwining theory.

Fullness and Connes' $\boldsymbol{\tau}$ invariant of type III tensor product factors · Unique McDuff decomposition: proof of Theorem [ref] · 0.93

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