L2-rigidity in von Neumann algebras

By J. Peterson. 2009

121 citations recorded by the source corpus.

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/e08ce5d144cbbc23a65a98420e686f87b6815d5d

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Algebra and Number Theory

1. Adrian Ioana
2. S. Vaes
3. Cyril Houdayer
4. Sorin Popa
5. I. Chifan
6. Thomas Sinclair
7. J. Peterson
8. Ben Hayes

In Geometry and Topology

1. Adrian Ioana
2. S. Vaes
3. Cyril Houdayer
4. Thomas Sinclair
5. I. Chifan
6. Sorin Popa
7. J. Peterson
8. Ben Hayes

In Mathematical Physics

1. Adrian Ioana
2. S. Vaes
3. Cyril Houdayer
4. Sorin Popa
5. Thomas Sinclair
6. I. Chifan
7. J. Peterson
8. Javier Parcet

Citations in the corpus

• On a class of II1 factors with at most one Cartan subalgebra, II (2010, unknown): “[Pet09]).”
• Group cocycles and the ring of affiliated operators (2007, background): “Some evidence for this appears in [25, 36], and in [35].”
• A random matrix approach to the Peterson-Thom conjecture (2020, background): “For example, primeness of all nonamenable subfactors [56], as well as the celebrated strong solidity of free group factors [53].”
• On the superrigidity of malleable actions with spectral gap (2006, background): “factors M that cannot be decomposed as tensor products M = Q⊗Q0 with Q, Q0 II1 factors (see [O1], [O2], [ Pe ] for other examples of such factors):”
• Type III factors with unique Cartan decomposition (2012, methodology): “r forms of deformation for Γ. The article [OP08] covered groups Γ with the complete metric approximation property and a proper 1-cocycle into a nonamenable representation, by using the deformation of [Pe06] associated with a densely defined derivation. In [Oz10], it was shown that in order to prove w”
• A free stochastic partial differential equation (2010, unknown): “) where we define T α= ∆˜˜η /2αthe contraction commuting with ∆˜1/2 so that we also get S(Z) ≤ C′′||∆˜1/2(Z)|| 2||Z||2 <∞. Using the formula η1/2 α = π−1 R∞ 0 t−1/2 1+t ηα(1+t)/tdt(cf. lemma 2.2 in [36], for brevity we write αt = α(1+t)/t≥ α), one deduces δi˜η 1/2 α (Z) = ˜η⊗1/2 α δi(Z)− 1 απ Z∞ 0”
• Group measure space decomposition of II1 factors and W*-superrigidity (2009, background): “sion function is all [0, 1 ], the group F(M) seems to always be equal to R+. Supporting evidence comes from the case M = L ∞ (X) � � with � amenable,”
• ON THE STRUCTURAL THEORY OF II1 FACTORS OF NEGATIVELY CURVED GROUPS, II. ACTIONS BY PRODUCT GROUPS (2011, methodology): “En devéloppant une nouvelle approche, qui combine les méthodes de Peterson [29], d’Ozawa et Popa [27, 28], et d’Ozawa [25], nous renforçons ce résultat en montrant que ce facteur est fortement solide.”
• On cocycle superrigidity for Gaussian actions (2009, background): “However, this extra condition was not used in [29], and since the above definition has better stability properties (see Theorem 6.”
• W*-superrigidity for Bernoulli actions of property (T) groups (2010, methodology): “He considered profinite actions of certain groups having infinite subgroups with the relative property (T) and used, among other things, techniques and results from [30], [28], [15].”
• Smooth Fourier multipliers on group von Neumann algebras (2010, background): “sume that the set of elements 6 JUNGE, MEI AND PARCET f∈ M such that the gradient Γ(f,f) = L1 − lim t→0 St(f∗f)+f∗f−St(f∗)f−f∗St(f) 2t exist in L1 —both for fand f∗— is weakly dense in M. We refer to [15, 67] for more information on gradients, or as Meyer’s calls them “carr´e du champs”. Under that ”