2,917,806 research outputs found

    Derivations in the Banach ideals of Ï„\tau-compact operators

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    Let M\mathcal{M} be a von Neumann algebra equipped with a faithful normal semi-finite trace τ\tau and let S0(τ)S_0(\tau) be the algebra of all τ\tau-compact operators affiliated with M\mathcal{M}. Let E(τ)⊆S0(τ)E(\tau)\subseteq S_0(\tau) be a symmetric operator space (on M\mathcal{M}) and let E\mathcal{E} be a symmetrically-normed Banach ideal of τ\tau-compact operators in M\mathcal{M}. We study (i) derivations δ\delta on M\mathcal{M} with the range in E(τ)E(\tau) and (ii) derivations on the Banach algebra E\mathcal{E}. In the first case our main results assert that such derivations are continuous (with respect to the norm topologies) and also inner (under some mild assumptions on E(τ)E(\tau)). In the second case we show that any such derivation is necessarily inner when M\mathcal{M} is a type II factor. As an interesting application of our results for the case (i) we deduce that any derivation from M\mathcal{M} into an LpL_p-space, Lp(M,τ)L_p(\mathcal{M},\tau), (1<p<∞1<p<\infty) associated with M\mathcal{M} is inner

    Raising and lowering operators and their factorization for generalized orthogonal polynomials of hypergeometric type on homogeneous and non-homogeneous lattice

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    We complete the construction of raising and lowering operators, given in a previous work, for the orthogonal polynomials of hypergeometric type on non-homogeneous lattice, and extend these operators to the generalized orthogonal polynomials, namely, those difference of orthogonal polynomials that satisfy a similar difference equation of hypergeometric type.Comment: LaTeX, 19 pages, (late submission to arXiv.org

    Commutator estimates in W∗W^*-factors

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    Let M\mathcal{M} be a W∗W^*-factor and let S(M)S\left( \mathcal{M} \right) be the space of all measurable operators affiliated with M\mathcal{M}. It is shown that for any self-adjoint element a∈S(M)a\in S(\mathcal{M}) there exists a scalar λ0∈R\lambda_0\in\mathbb{R}, such that for all ε>0\varepsilon > 0, there exists a unitary element uεu_\varepsilon from M\mathcal{M}, satisfying ∣[a,uε]∣≥(1−ε)∣a−λ01∣|[a,u_\varepsilon]| \geq (1-\varepsilon)|a-\lambda_0\mathbf{1}|. A corollary of this result is that for any derivation δ\delta on M\mathcal{M} with the range in an ideal I⊆MI\subseteq\mathcal{M}, the derivation δ\delta is inner, that is δ(⋅)=δa(⋅)=[a,⋅]\delta(\cdot)=\delta_a(\cdot)=[a,\cdot], and a∈Ia\in I. Similar results are also obtained for inner derivations on S(M)S(\mathcal{M}).Comment: 21 page

    The Competitive Advantage of Outstanding the Products and Services of the Nigerian Service Industry

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    The study examines the concept of outsourcing and the possible impact it has on the competitive advantage it has on a company in Nigerian economy. Outsourcing is the practice in which companies move or contract out some or all of their products or service operations to other companies that specialize in those operations or to companies in other countries. The problems indentified in the Nigeria service industry are high operating cost having negative impact on return on capital employed, sub-optimality in production because of ineffective utilization of resources and inability of organization to identify areas of core competence for competitive advantage. The main objective of this paper is to evaluate the competitive advantag

    On the deformation of abelian integrals

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    We consider the deformation of abelian integrals which arose from the study of SG form factors. Besides the known properties they are shown to satisfy Riemann bilinear identity. The deformation of intersection number of cycles on hyperelliptic curve is introduced.Comment: 8 pages, AMSTE

    Black branes in asymptotically Lifshitz spacetime and viscosity/entropy ratios in Horndeski gravity

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    We investigate black brane solutions in asymptotically Lifshitz spacetime in 3+1-dimensional Horndeski gravity, which admit a critical exponent fixed at z=1/2z=1/2. The cosmological constant depends on zz as Λ=−(1+2z)/L2\Lambda=-(1+2z)/L^{2}. We compute the shear viscosity in the 2+1-dimensional dual boundary field theory via holographic correspondence. We investigate the violation of the bound for viscosity to entropy density ratio of η/s≥1/(4π)\eta/s\geq1/(4\pi) at z=1/2z=1/2.Comment: 7 pages, no figures, 1 table. Version published in EP
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