170,590 research outputs found
A comparison between the max and min norms on C∗(Fn)⊗C∗(Fn).
No full textAbstract. Let Fn, n > 2, be the free group on n generators, denoted by U1,U2, . . . ,Un. Let C¤(Fn) be the full C¤-algebra of Fn. Let X be the
vector subspace of the algebraic tensor product C(Fn) C¤(Fn), spannedby 1 1,U1 1, . . . ,Un 1, 1 U1, . . . , 1 Un. Let k · kmin and k · kmax be
the minimal and maximal C¤ tensor norms on C¤(Fn)C¤(Fn), and use the
same notation for the corresponding (matrix) norms induced on Mk(C)X,
k 2 N.
Identifying X with the subspace of C¤(F2n) obtained by mapping U1
1, . . . , 1Un into the 2n generators and the identity into the identity, we get
a matrix norm k · kC¤(F2n) which dominates the k · kmax norm on Mk(C)X.
In this paper we prove that, with N = 2n + 1 = dimX, we have
kXkmax 6 kXkC¤(F2n) 6 (N2 − N)1/2kXkmin, X 2 Mk(C)
A type IIIλ factor with core isomorphic to the von Neumann algebra of a free group, tensor B(H)
No full textThe author constructs a free product of M2(C) with a non-tracial state and L∞(0,1) with Lebesgue measure. He shows that this is a factor of type IIIλ with λ∈(0,1) and that the core of this factor is isomorphic to the tensor product of B(H) and L(F∞), the II1 factor of the free group on infinitely many generators
A universal, non-commutative C∗-algebra associated to the Hecke algebra of double cosets
No full textLet G be a discrete group and Γ an almost normal subgroup. The operation of cosets concatanation extended by linearity gives rise to an operator system that is embeddable in a natural C* algebra. The Hecke algebra naturally embeds as a diagonal of the tensor product of this algebra with its opposite. When represented on the l2 space of the group, by left and right convolution operators, this representation gives rise to abstract Hecke operators that in the modular group case, are unitarily equivalent to the classical operators on Maass wave form
Anisotropic Navier Kirchhoff problems with convection and Laplacian dependence
No full textWe consider the Navier problem-Delta(2)(k,p)u(x)=f(x,u(x), del u(x), Delta u(x)) in Omega, u vertical bar(partial derivative Omega) =Delta u vertical bar(partial derivative Omega) = 0,driven by the sign-changing (degenerate) Kirchhoff type p(x)-biharmonic operator, and involving a (del u, Delta u)-dependent nonlinearity f. We prove the existence of solutions, in weak sense, defining an appropriate Nemitsky map for the nonlinearity. Then, the Brouwer fixed point theorem assessed for a Galerkin basis of the Banach space W-2,W-p(x)(Omega)boolean AND W-0(1,p(x))(Omega) leads to the existence result. The case of nondegenerate Kirchhoff type p(x)-biharmonic operator is also considered with respect to the theory of pseudo-monotone operators, and an asymptotic analysis is derived
Conformal nets, maximal temperature and models from free probability
No full textWe consider conformal nets on S-1 of von Neumann algebras, acting on the full Fock space, arising in Free Probability. These models are twisted local, but non-local. We extend to the non-local case the general analysis of the modular structure. The local algebras turn out to be III1-factors associated with free groups. We use our setup to show examples exhibiting arbitrarily large maximal temperatures, but failing to satisfy the split property, then clarifying the relation between the latter property and the trace class conditions on e(-betaL), where L is the conformal Hamiltonian
The Corporate Tax Reform of 2008: Germany’s Answer to Globalization – or Just Patchwork?
No full textUnternehmensbesteuerung, Steuerreform, Wirtschaftliche Anpassung, Globalisierung, Wirtschaftspolitische Wirkungsanalyse, Deutschland, Corporate taxation, Tax reform, Economic adjustment, Globalization, Economic policy analysis, Germany
A Mixing Property for the Action of SL(3,Z) × SL(3,Z) on the Stone–Čech Boundary of SL(3,Z)
No full textBy analogy with the construction of the Furstenberg boundary, the Stone- C?ech boundary of SL(3, Z) is a fibered space over products of projective matrices. The proximal behaviour on this space is exploited to show that the preimages of certain sequences have accumulation points that belong to specific regions, defined in terms of flags. We show that the SL(3, Z) x SL(3, Z)-quasi-invariant Radon measures supported on these regions are tempered. Thus, every quasi-invariant Radon boundary measure for SL(3, Z) is an orthogonal sum of a tempered measure and a measure having matrix coefficients belonging to a certain ideal c' (0)((SL(3, Z) x SL(3, Z)), slightly larger than c(0)((SL(3, Z) x SL(3, Z)). Hence, the left-right representation of C-*(SL(3, Z) x SL(3, Z)) in the Calkin algebra of SL(3, Z) factors through C-* (c' 0)(SL(3, Z) x SL(3, Z)) and the centralizer of every infinite subgroup of SL(3, Z) is amenable
Irreducible subfactors derived from Popa's construction for non-tracial state
No full textFor an inclusion of the form C⊆Mn(C)
, where M n (C) is endowed with a state with diagonal weights λ = (λ1, ..., λn), we use Popa’s construction, for non-tracial states, to obtain an irreducible inclusion of II1 factors, Nλ(Q)⊆Mλ(Q)
of index ∑1λi
. Mλ(Q) is identified with a subfactor inside the centralizer algebra of the canonical free product state on Q ⋆ M N (C). Its structure is described by “infinite” semicircular elements as in {xc[32]}.
The irreducible subfactor inclusions obtained by this method are similar to the first irreducible subfactor inclusions, of index in [{xc4},∞) constructed in {xc[24]}, starting with the Jones’ subfactors inclusion Rs⊆R
, s gt; 4. In the present paper, since the inclusion we start with has a simpler structure, it is easier to control the algebra structure of the subfactor inclusions.
If the weights correspond to a unitary, finite-dimensional representation of a Woronowicz’s compact quantum group G, then the factor Mλ(Q) is contained in the fixed point algebra of an action of the quantum group on Q ⋆ MN(C), with equality if G is SUq(N), (or SOq(3) when N = 2). By Takesaki duality, the factor Mλ(L(FN)) is Morita equivalent to
L
(F∞).
This method gives also another approach to find, as also recently proved in {xc[36]}, irreducible subfactors of
L
(F∞) for index values bigger than 4
Management of venous thrombosis in the pediatric patient
No full textVlad C Radulescu Department of Pediatrics, University of Kentucky, Lexington, KY, USA Abstract: The incidence of venous thromboembolism in children has increased significantly over the past decade. The evaluation and management of the child with venous thromboembolism, while based on the adult experience, has its own particularities dictated by the differences in the hemostatic system of the newborn and child. The current review addresses the evaluation of pediatric patient with thrombosis as well as the established and emerging treatment interventions. Keywords: venous thromboembolism, children, anticoagulant therapy, thrombolytic therap
A remark on supra-additive and supra-multiplicative operators on
No full textsummary:M. Radulescu proved the following result: Let be a compact Hausdorff topological space and a supra-additive and supra-multiplicative operator. Then is linear and multiplicative. We generalize this result to arbitrary topological spaces
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