On spinors

For a 2^n-dimensional complex Hermitian vector space S, we prove that any unitary basis of S can be explained as an augmented spinor structure on S. By using this explanation, a SpinC（2n）- action on S is equivalent to an action on a subset of augmented spinor structures. The latter action is a little easy to be understood, and is shown in the last part of this paper. Such kind of understanding could be of use to the discussions of Hermitian manifolds and spin manifolds, especially could help to find connections and elliptical operators.     

超市全球浪潮

跨国零售商成功拓展的诀窍是什么？陷入困境的公司又该如何化险为夷？英国最大的零售商特斯科乐购（Tesco）投资者关系总监SteveWebb表示．对那些境外扩张的零售运营商来说,尤其是餐饮类公司,其成败主要取决于是否满足当地顾客的特殊需求。做到这一点其实很容易：雇佣当地人当主管则可。Webb介绍到．“在海外业务中我们总共有160000名员工．但仅有180名是由英国派出。”     

Estimates of three classical summations on the spaces F_p~(α,q)(R~n)(0 < p ≤ 1)

We obtain the boundedness on ˙Fα,qp(Rn) for the Poisson summation and Gauss summation. Their maximal operators are proved to be bounded from˙Fα,qp(Rn) to L∞(Rn).For the maximal operator of the Bochner-Riesz summation, we prove that it is bounded from˙Fα,qp(Rn) to Lpnn-pα,∞(Rn).     

Dual Toeplitz operators on the sphere

Dual Toeplitz operators on the Hardy space of the unit circle are anti-unitarily equivalent to Toeplitz operators. In higher dimensions, for instance on the unit sphere, dual Toeplitz operators might behave quite differently and, therefore, seem to be a worth studying new class of Toeplitz-type operators. The purpose of this paper is to introduce and start a systematic investigation of dual Toeplitz operators on the orthogonal complement of the Hardy space of the unit sphere in Cn . In particular, we establish a corresponding spectral inclusion theorem and a Brown-Halmos type theorem. On the other hand, we characterize commuting dual Toeplitz operators as well as normal and quasinormal ones.     

AREA INTEGRAL FUNCTIONS AND H∞ FUNCTIONAL CALCULUS FOR SECTORIAL OPERATORS ON HILBERT SPACES

Area integral functions are introduced for sectorial operators on Hilbert spaces. We establish the equivalence relationship between the square and area integral functions. This immediately extends McIntosh/Yagi＇s results on H∞ functional calculus of sectorial operators on Hilbert spaces to the case when the square functions are replaced by the area integral functions.     

APPROXIMATING SOLUTION OF 0∈ T（x） FOR AN H-MONOTONE OPERATOR IN HILBERT SPACES

The purpose of this paper is to study the solution of 0 ∈ T (x) for an H-monotone operator introduced in [Fang and Huang, Appl. Math. Comput. 145(2003)795-803] in Hilbert spaces, which is the first pro...     

Multilinear fractional Hausdorff operators

In this paper,by introducing the space with weak mixed norms,weak type estimates of two kinds of multilinear fractional Hausdorff operators RΦ,β and SΦ,β on Lebesgue spaces are shown.By virtue of Marcinkiewicz interpolation,strong type estimates of these two operators on Lebesgue spaces are also obtained.Our methods shed some new light on dealing with the case of non-radial function Φ.     

Von Neumann Algebras Associated with the Group SL2（R）

Let M\mathcal{M} and N\mathcal{N} be the von Neumann algebras induced by the rational action of the group SL ₂(ℝ) and its subgroup P on the upper half plane \mathbbH\mathbb{H}. We have shown that N\mathcal{N} is spatial isomorphic to the group von Neumann algebra L_P\mathcal{L}_P and characterized M\mathcal{M} and its commutant M￠\mathcal{M}' and gotten a generalization of the Mautner’s lemma. It is also shown that the Berezin operator commutates with the Laplacian operator.     

A LIL and limit distributions for trimmed sums of random vectors attracted to operator semi-stable laws

Let θ∈ Rdbe a unit vector and let X,X1,X2,...be a sequence of i.i.d.Rd-valued random vectors attracted to operator semi-stable laws.For each integer n ≥ 1,let X1,n ≤···≤ Xn,n denote the order statistics of X1,X2,...,Xn according to priority of index,namely | X1,n,θ | ≥···≥ | Xn,n,θ |,where ·,· is an inner product on Rd.For all integers r ≥ 0,define by(r)Sn = n-ri=1Xi,n the trimmed sum.In this paper we investigate a law of the iterated logarithm and limit distributions for trimmed sums(r)Sn.Our results give information about the maximal growth rate of sample paths for partial sums of X when r extreme terms are excluded.A stochastically compactness of(r)Sn is obtained.