Ji Gao
Department of Mathematics
Community College of Philadelphia
1700 Spring Garden St., Philadelphia, PA 191303991, U.S.A.
jgao@ccp.edu
Abstract : In this talk the properties of some parameters in Banach spaces are discussed, the relationship between these parameters and normal structure are studied, and some well known results are improved.
Zhangjian Hu
Department of Mathematics
Huzhou Teachers College
Huzhou, Zhejiang, 313000, P.R.China
huzj@mail.huptt.zj.cn
Abstract : Let W Ì R^{n} be a bounded convex domain with C^{2} boundary. And given 0 < p, q £ ¥ and a normal weight function j(r), let H_{p, q, j} be the harmonic mixed norm space on W. We prove that the Gleason's problem (W, a, H_{p, q,j}) is always solvable for any reference point a Î W. Also, the Gleason's problem for the harmonic jBloch (little jBloch) space is solvable. The parallel results for the holomorphic functions on bounded convex domains in C^{n} are obtained.
Guoxing Ji
College of Mathematics and Information Science
Shaanxi Normal University
Xi'an, 710062, P. R. China
gxji@snnu.edu.cn
Abstract : In this talk, we consider algebraic commutants of certain analytic operator algebras. Let H be a Hilbert space and let B(H) be the algebra of all bounded linear operators. For a subset E of B(H), we denote by E^{¢} the algebraic commutant, that is

Let M be a sfinite von Neumann algebra on H and let A be either a maximal subdiagonal algebra of M with respect to a faithful normal expectation F from M onto the diagonal D of A or an analytic operator algebra determined by a flow on M. We prove that the algebraic commutants A^{¢} of A is selfadjoint, that is, A^{¢} = M^{¢}. This may regard as an algebraic version of Fuglede's Theorem.
Genaro López
Department of Mathematics
Universidad de Sevilla
Seville 41080, Spain
glopez@us.es
Abstract : The paper is concerned with the study of those subsets of spaces of continuous and bounded functions for which it is possible to find a nonexpansive selection of the metric projection. We first characterize those hyperplanes of these spaces with the above property. Later we use these results in order to find more general subsets with the same property.
Zengjian Lou
Department of Mathematics
Shantou University
Guangdong Shantou 515063
P. R. China
zjlou@stu.edu.cn
Abstract : Let W be the Eucliden space R^{n}, the upper halfspace R^{n}_{+}, a special Lipschitz domain or a bounded strongly Lipschitz domain in R^{n}. Divergencefree Hardy spaces H^{1}_{z,div}(W, R^{n}) on W is the space of divergencefree functions in Hardy space H^{1}(R^{n}, R^{n}) with support in W. We exhibit an divergencefree atomic decomposition and use this to characterize the dual space, and prove a ``divcurl'' type theorem on W. As applications we prove an atomic decomposition for the HardySobolev space and give coercivity properties for some polyconvex forms.
The main results are:
Atomic Decomposition: f Î H^{1}_{z,div}(W, R^{n}) if and only if it can be written as a sum of H^{1}_{z,div}(W, R^{n})atoms.
Dual Space:

DivCurl Type Theorem on W: Let b Î L^{2}_{loc}(W, R^{n}). Then

ChiKeung Ng
Department of Mathematics
Nankai University
ckng@nankai.edu.cn
Abstract : We will give a characterization of operator spaces amongst all Banach K(l^{2})bimodules, a characterization of M_{n}(\BbbC)bimodule that can be extended to an operator space structure as well as a characterization of (F)Banach bundles amongst all (H)Banach bundles over a hyperStonian space. All these three characterizations depend on whether certain natural map from a Banach bimodules to its canonical bidual being isometric.
Pengcheng Niu
Department of Applied Mathematics
Northwestern Polytechnical University
Xi'an, Shanxi, P.R.China
pengchengniu@yahoo.com.cn
Abstract : In this talk we introduce the Hardy type inequalities on the Heisenberg group via the Picone type identities of psubLaplacians. Some new results are obtained.
Tao Qian
Department of Mathematics
University of Macau
P.O. Box 3001, Macao
fsttq@umac.mo
Abstract : To answer a question in relation to analytic signals in timefrequency analysis we prove that an analytic function is an inner function in the unit disc or in the upperhalf complex plane if and only if the imaginary part of its boundary value is the Hilbert transform of its real part.
Jiong Sun^{*}
Department of Mathematics
Inner Mongolia university
Huhhot 010021 P.R.China
masun@imu.edu.cn
D.E. Edmunds
Department of Mathematics
Mantell Building
University of Sussex
Brighton BN1 9RF, U.K.
D.E.Edmunds@sussex.ac.uk
Aiping Wang
Department of Mathematics
Inner Mongolia university
Huhhot 010021 P.R.China
Abstract : In this paper, we obtain some results on the relationship among essential spectrum, deficiency index of M,where M is a 2Norder differential operator, and the number of solutions of My = ly in L^{2}[a,+¥). It is proved that for every l Î I if the number of Dirichlet solution of (MlI)f = 0 is N (their deficiency indices may be in middle case ), then continuous spectrum of H is empty in I , where H is a self adjoint operator associated with M . Furthermore if point spectrum has not accumulation point in I , then essential spectrum s_{e}(H) ÇI = Æ for every selfadjoint operator H associated with M. The results extent Weidmann's result in the limitpoint case ( minimal deficiency indices ) to the middle deficiency indices cases.
Xiangxing Tao
Faculty of Science
Ningbo University
Ningbo, Zhejiang, 315211, P.R. China
taoxiangxing@nbu.edu.cn
Abstract : Let u be a solution to a second order elliptic equation with singular potentials belonging to the KatoFeRermanPhong's class in Lipschitz domains, an elementary proof of the doubling property for u^{2} over balls is presented, if the balls contain in the domain or center at some points near some open subset of the boundary on which the solution u vanishes continuously. Moreover, we found the inner unique continuation theorems and the boundary unique continuation theorems for the elliptic equations.
Guojun Wang
Institute of Mathematics
Shaanxi Normal University
Xi'an 710062, China
gjwang@snnu.edu.cn
Abstract : It is proved that linear structures can be constructed by means of metrics on translation spaces under certain conditions. The concept of subnormed Zlinear spaces is introduced and it is clarified that a translation space is a subnormed Zlinear space if and only if its translation group is Abelian. Analogues of the bounded linear operator theorem, the HahnBanach theorem and the resonance theorem are established in subnormed Zlinear space.
Metrics can induce topologies on a given nonempty set X and different metrics may induce different topologies on X. An interesting question is: Can metrics induce linear structures on X? The aim of the present paper is to answer this question.
The concept of a translation space (X,T) is introdued in [2], where T is the translation group. A much more general form of the Scheeffer's theorem in point set topology has been established in translation spaces, while this paper stresses linear properties rather than topological properties. We prove that a linear structure with coefficients in the ring Z of integers can be endowed with X if T is an Abelian group, and the resulted space is called a subnormed Zlinear space, briefly, a Zspace. Propositions that are analogues of the bounded linear operator theorem, the HahnBanach theorem, and the resonance theorem respectively are obtained in Zspaces. In section 1, concepts related to translation spaces are briefly introduced which are necessary for the subsequent sections. In section 2, bounded, locally bounded, and continuous operators and their relations are discussed in commutative translation spaces. Section 3 deals with a generalization of the HahnBanach theorem and section 4 deals with that of the resonance theorem.Lastly, section 5 is conclusion.
Key words translation space; subnormed Zlinear space; HahnBanach theorem; resonance theorem
Reference
[1] J.L.Kelley, General Topology, SpringerVerlag, 1955, New York.
[2] Guojun Wang, Wei Wang, Generalization of the Scheeffer's theorem, Indian J. Math., 1999,41(3):407414.
[3] A. Wilansky, Functional Aanlysis, Blaisdell Publishing Company, 1964, New York.
Zhijian Wu
Department of Mathematics
The University of Alabama
Tuscaloosa, Alabama 35487, U.S.A.
zwu@bama.ua.edu
Abstract : We study a class of Volterra type operators on analytic functions. We characterize the boundedness and compactness of the operator in terms of its symbol function.
Yueping Zhu
Department of Mathematics
Nantong University
Nantong City, Jiangsu Province 226007, P.R. China
zhuyueping@ntu.edu.cn
Joint work with Tom ter Elst, Derek W Robinson and Adam Sikora
Abstract : We consider properties of secondorder operators H = å^{d}_{ij, = 1} ¶_{i} c_{ij}¶_{j} on \Bbb R^{d} with bounded real symmetric measurable coefficients. We assume that C = (c_{ij}) ³ 0 almost everywhere, but allow for the possibility that C is singular. We associated with H a canonical selfadjoint viscosity operator H_{0} and examine properties of the viscosity semigroup S^{(0)} generated by H_{0}. The semigroup extends to a positive contraction semigroup on the L_{p}spaces with p Î [1,¥]. It conserves probability, satisfies L_{2} offdiagonal bounds and the wave equation associated with H_{0} has finite speed of propagation. Nevertheless S^{(0)} is not always strictly positive, this demonstrates that subelliptic semigroups are not ergodic in general and their kernels are neither strictly positive nor Hölder continuous. In particular one can construct examples for which both upper and lower Gaussian bounds fail even with coefficients in C^{2e} (\Bbb R^{d}) with e > 0.