Results 1  10
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12
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.
Embeddings of discrete groups and the speed of random walks
, 2007
"... Let G be a group generated by a finite set S and equipped with the associated leftinvariant word metric dG. For a Banach space X let α ∗ X (G) (respectively α # X (G)) be the supremum over all α ≥ 0 such that there exists a Lipschitz mapping (respectively an equivariant mapping) f: G → X and c> ..."
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Cited by 25 (4 self)
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Let G be a group generated by a finite set S and equipped with the associated leftinvariant word metric dG. For a Banach space X let α ∗ X (G) (respectively α # X (G)) be the supremum over all α ≥ 0 such that there exists a Lipschitz mapping (respectively an equivariant mapping) f: G → X and c> 0 such that for all x, y ∈ G we have ‖ f (x) − f (y) ‖ ≥ c · dG(x, y) α. In particular, the Hilbert compression exponent (respectively the equivariant Hilbert compression exponent) of G is α ∗ (G) ≔ α ∗ (G) (respectively
On the association of sum– and max–stable processes
 Statistics and Probability Letters
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ISOMETRIES OF LpSPACES OF SOLUTIONS OF HOMOGENEOUS PARTIAL DIFFERENTIAL EQUATIONS
, 1993
"... Abstract. Let n ≥ 2, A = (aij) n i,j=1 be a real symmetric matrix, a = (ai) n i=1 ∈ Rn. Consider the differential operator DA = ∑ n ∂ 2 ∂x i∂x j + ∑ n ai ∂x i. Let E be i,j=1 aij i=1 a bounded domain in Rn, p> 0. Denote by L p D (E) the space of solutions of the A equation DAf = 0 in the domain ..."
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Cited by 1 (1 self)
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Abstract. Let n ≥ 2, A = (aij) n i,j=1 be a real symmetric matrix, a = (ai) n i=1 ∈ Rn. Consider the differential operator DA = ∑ n ∂ 2 ∂x i∂x j + ∑ n ai ∂x i. Let E be i,j=1 aij i=1 a bounded domain in Rn, p> 0. Denote by L p D (E) the space of solutions of the A equation DAf = 0 in the domain E provided with the Lpnorm. We prove that, for matrices A, B, vectors a, b, bounded domains E, F, and every p> 0 which is not an even integer, the space L p D (E) is isometric to a subspace of A L p
Statement of Results
"... Abstract. We present three results on isometric embeddings of a (closed, linear) subspace X of Lp = Lp[0; 1] into ‘p. First we show that if p =2 2N, then X is isometrically isomorphic to a subspace of ‘p if and only if some, equivalently every, subspace of Lp which contains the constant functions an ..."
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Abstract. We present three results on isometric embeddings of a (closed, linear) subspace X of Lp = Lp[0; 1] into ‘p. First we show that if p =2 2N, then X is isometrically isomorphic to a subspace of ‘p if and only if some, equivalently every, subspace of Lp which contains the constant functions and which is isometrically isomorphic to X, consists of functions having discrete distribution. In contrast, if p 2 2N and X is flnite dimensional, then X is isometrically isomorphic to a subspace of ‘Np, where the positive integer N depends on the dimension of X, on p, and on the chosen scalar fleld. The third result, stated in local terms, shows in particular that if p is not an even integer, then no flnite dimensional Banach space can be isometrically universal for the 2 dimensional subspaces of Lp.
1 Quantifier elimination in the theory of Lp(Lq)Banach lattices
"... Abstract: We introduce the class of doubly atomless bands in Lp(Lq)Banach lattices and show that this class is axiomatizable by positive bounded sentences in the language of Banach lattices. (Here p 6 = q are fixed and in the interval 1 ≤ p, q < ∞.) The theory of this class is complete (indeed, ..."
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Abstract: We introduce the class of doubly atomless bands in Lp(Lq)Banach lattices and show that this class is axiomatizable by positive bounded sentences in the language of Banach lattices. (Here p 6 = q are fixed and in the interval 1 ≤ p, q < ∞.) The theory of this class is complete (indeed, we show it is separably categorical) and model complete. Further, we show that it satisfies quantifier elimination if and only if the ratio p/q is not an integer. On the functional analytic side, the proof of the latter result uses a positivecoefficient version of the well known RudinPlotkinHardin extension theorems.
STOCHASTIC INTEGRAL REPRESENTATIONS AND CLASSIFICATION OF SUM – AND MAX–INFINITELY DIVISIBLE PROCESSES
"... Abstract. We introduce the notion of minimality for spectral representations of sum – and max– infinitely divisible processes and prove that the minimal spectral representation on a Borel space exists and is unique. This fact is used to show that a stationary, stochastically continuous, sum– or max– ..."
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Abstract. We introduce the notion of minimality for spectral representations of sum – and max– infinitely divisible processes and prove that the minimal spectral representation on a Borel space exists and is unique. This fact is used to show that a stationary, stochastically continuous, sum– or max–i.d. random process on Rd can be generated by a measure–preserving flow on a σ–finite Borel measure space and that this flow is unique. This development makes it possible to extend the classification program of Rosiński [30] with a unified treatment of both sum – and max–infinitely divisible processes. As a particular case, we characterize stationary, stochastically continuous, union–infinitely divisible random subsets of Rd. We introduce and classify several new max–i.d. random field models including fields of Penrose type and fields associated to Poisson line processes. 1.