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Interpolated free group factors
 Pacific J. Math
, 1994
"... Abstract. The interpolated free group factors L(Fr) for 1 < r ≤ ∞, (also defined by F. Rădulescu) are given another (but equivalent) definition as well as proofs of their properties with respect to compression by projections and free products. In order to prove the addition formula for free produ ..."
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Cited by 60 (4 self)
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Abstract. The interpolated free group factors L(Fr) for 1 < r ≤ ∞, (also defined by F. Rădulescu) are given another (but equivalent) definition as well as proofs of their properties with respect to compression by projections and free products. In order to prove the addition formula for free products, algebraic techniques are developed which allow us to show R∗R ∼ = L(F2) where R is the hyperfinite II1–factor. Introduction. The free group factors L(Fn) for n = 2, 3,..., ∞ (introduced in [4]) have recently been extensively studied [11,2,5,6,7] using Voiculescu’s theory of freeness in noncommutative probability spaces (see [8,9,10,11,12,13], especially the latter for an overview). One hopes to eventually be able to solve the old isomorphism question, first raised by R.V. Kadison in the 1960’s, of whether L(Fn) ∼ = L(Fm) for n ̸ = m. In [7], F. Rădulescu introduced
Property (T) and rigidity for actions on Banach spaces
 BHV] [BoS] [Bou] [BuSc] [BuSc’] [BrSo] [C] M. B. Bekka, P. de la Harpe, Alain Valette. “Kazhdan’s
, 2005
"... Abstract. We study property (T) and the fixed point property for actions on L p and other Banach spaces. We show that property (T) holds when L 2 is replaced by L p (and even a subspace/quotient of L p), and that in fact it is independent of 1 ≤ p < ∞. We show that the fixed point property for L ..."
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Cited by 52 (6 self)
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Abstract. We study property (T) and the fixed point property for actions on L p and other Banach spaces. We show that property (T) holds when L 2 is replaced by L p (and even a subspace/quotient of L p), and that in fact it is independent of 1 ≤ p < ∞. We show that the fixed point property for L p follows from property (T) when 1 < p < 2 +ε. For simple Lie groups and their lattices, we prove that the fixed point property for L p holds for any 1 < p < ∞ if and only if the rank is at least two. Finally, we obtain a superrigidity result for actions of irreducible lattices in products of general groups on superreflexive Banach spaces.
Strong rigidity of generalized Bernoulli actions and computations of their symmetry groups
, 2006
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Explicit computations of all finite index bimodules for a family of II1 factors
 CARTAN SUBALGEBRAS OF AMALGAMATED FREE PRODUCT II1 FACTORS 47
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Factors of type II1 without nontrivial finite index subfactors, preprint math.OA/0610231
, 2006
"... We call a subfactor N ⊂ M trivial if it is isomorphic with the obvious inclusion of N in Mn(C) ⊗ N. We prove the existence of type II1 factors M without nontrivial finite index subfactors. Equivalently, every MMbimodule with finite coupling constant, both as a left and as a right Mmodule, is a ..."
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Cited by 22 (8 self)
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We call a subfactor N ⊂ M trivial if it is isomorphic with the obvious inclusion of N in Mn(C) ⊗ N. We prove the existence of type II1 factors M without nontrivial finite index subfactors. Equivalently, every MMbimodule with finite coupling constant, both as a left and as a right Mmodule, is a multiple of L 2 (M). Our results rely on the recent work of Ioana, Peterson and Popa, who proved the existence of type II1 factors without outer automorphisms.