Normal extensions of semigroups of operators to Krein spaces

In this paper, we prove that every strongly continuous semigroup of bounded operators on a Hilbert space may be extended to a strongly continous semigroup of normal operators on a larger Krein space. Several equivalent formulations for the case where the extension space is a Pontrjagin space are given.     

p-距离空间中的一类压缩映象的不动点定理

仿照距离空间,2-距离空间中的一些概念,引入了p-距离空间及p-距离空间中的一些基本概念.根据研究2-距离空间中不动点理论的思想和方法,利用泛函分析的理论,对p-距离空间中的不动点问题进行了研究.把2.距离空间中压缩型映像的不动点理论移植到了p-距离空间中,形成了p-距离空间中压缩型映像的一些基本不动点理论.其距.离空...     

The dual of C ps (X)

This is a study of the dual space of continuous linear functionals on the function space C_ps(X) with a natural norm inherited from a larger Banach space. Here ps denotes the pseudocompact-open topology on C(X), the set of all real-valued continuous functions on a Tychonoff space X. The lattice structure and completeness of this dual space have been studied. Since this dual space is inherently related to a space of measures, the measure-theoretic characterization of this dual space has been studied extensively. Due to this characterization, a special kind of topological space, called pz-space, has been studied. Finally the separability of this dual space has been studied.      

Bloch spaces on bounded symmetric domains in complex Banach spaces Dedicated to Professor Sheng GONG on the occasion of his 75th birthday

We give a definition of Bloch space on bounded symmetric domains in arbitrary complex Banach space and prove such function space is a Banach space. The properties such as boundedness, compactness and closed range of composition operators on such Bloch space are studied.     

约束离散空间的试验设计方案研究

目前的试验设计大体在连续空间或者无约束的离散空间下进行研究,但实际工程中不少场景都需要在离散空间中挑选试验点来进行试验设计,通常的试验设计方法无法应用于约束的离散空间中.文章立足于实际工程背景,基于连续空间下的均匀试验设计,采用Gale-Shapley算法,给出了连续空间到离散空间的映射设计方案.最后,结合实例进行了Gale-Shapley算法与经验方法所得设计的对比验证研究,在约束的离散空间下,Gale-Shapley算法所得到的映射设计具有更好的均匀性,且计算效率满足工程实际需求.     

Reducing subspaces of multiplication operators on function spaces

This survey presents the brief history and recent development on commutants and reducing subspaces of multiplication operators on both the Hardy space and the Bergman space, and von Neumann algebras generated by multiplication operators on the Bergman space.     

A characterization of dual spaces

A Banach space is a dual space if and only if it is isometric to the space of uniform functions on a set with graded constraints.     

Aggregate preferred correspondence and the existence of a maximin REE

A general model of a pure exchange differential information economy is studied. In this economic model, the space of states of nature is a complete probability measure space, the space of agents is a finite measure space, and the commodity space is the Euclidean space. Under some appropriate and standard assumptions on agents' characteristics, results on continuity and measurability of the aggregate preferred correspondence similar to that of Aumann [8] are established. These results together with other techniques are then employed to prove the existence of a maximin rational expectations equilibrium (maximin REE) of the economic model.     

单位球面间的等距延拓

本文证明了在一定条件下赋范线性空间与其共轭空间的单位球面之间的等距算子可以延拓为全空间的实线性等距算子。进而,刻画了光滑的自反空间的单位球面到其共轭空间的单位球面上的等距算子。     

A family of symmetric mixed finite elements for linear elasticity on tetrahedral grids

A family of stable mixed finite elements for the linear elasticity on tetrahedral grids are constructed,where the stress is approximated by symmetric H(div)-Pk polynomial tensors and the displacement is approximated by C-1-Pk-1polynomial vectors,for all k 4.The main ingredients for the analysis are a new basis of the space of symmetric matrices,an intrinsic H(div)bubble function space on each element,and a new technique for establishing the discrete inf-sup condition.In particular,they enable us to prove that the divergence space of the H(div)bubble function space is identical to the orthogonal complement space of the rigid motion space with respect to the vector-valued Pk-1polynomial space on each tetrahedron.The optimal error estimate is proved,verified by numerical examples.     

Quantization of the Geodesic Flow on Quaternion Projective Spaces

We study a problem of the geometric quantization for the quaternionprojective space. First we explain a Kähler structure on the punctured cotangent bundleof the quaternion projective space, whose Kähler form coincides withthe natural symplectic form on the cotangent bundle and show thatthe canonical line bundle of this complex structure is holomorphicallytrivial by explicitly constructing a nowhere vanishing holomorphicglobal section. Then we construct a Hilbert space consisting of acertain class of holomorphic functions on the punctured cotangentbundle by the method ofpairing polarization and incidentally we construct an operatorfrom this Hilbert space to the L ₂ space of the quaternionprojective space. Also we construct a similar operator between thesetwo Hilbert spaces through the Hopf fiberation.We prove that these operators quantizethe geodesic flow of the quaternion projective space tothe one parameter group of the unitary Fourier integral operatorsgenerated by the square root of the Laplacian plus suitable constant.Finally we remark that the Hilbert space above has the reproducing kernel.     

Boundedness of Hardy-Littlewood maximal operator on block spaces with variable exponent

The family of block spaces with variable exponents is introduced. We obtain some fundamental properties of the family of block spaces with variable exponents. They are Banach lattices and they are generalizations of the Lebesgue spaces with variable exponents. Moreover, the block space with variable exponents is a pre-dual of the corresponding Morrey space with variable exponents. The main result of this paper is on the boundedness of the Hardy-Littlewood maximal operator on the block space with variable exponents. We find that the Hardy-Littlewood maximal operator is bounded on the block space with variable exponents whenever the Hardy-Littlewood maximal operator is bounded on the corresponding Lebesgue space with variable exponents.     

Geometric Gibbs theory In Memory of Professor Shantao Liao

We extend the classical Gibbs theory for smooth potentials to the geometric Gibbs theory for certain continuous potentials. We study the existence and uniqueness and the compatibility of geometric Gibbs measures associated with these continuous potentials. We introduce a complex Banach manifold structure on the space of these continuous potentials as well as on the space of all geometric Gibbs measures. We prove that with this complex Banach manifold structure, the space is complete and, moreover, is the completion of the space of all smooth potentials as well as the space of all classical Gibbs measures. There is a maximum metric on the space,which is incomplete. We prove that the topology induced by the newly introduced complex Banach manifold structure and the topology induced by the maximal metric are the same. We prove that a geometric Gibbs measure is an equilibrium state, and the infimum of the metric entropy function on the space is zero.     

Approximation of Hunt Processes by Multivariate Poisson Processes

We prove that arbitrary Hunt processes on a general state space can be approximated by multivariate Poisson processes starting from each point of the state space. The key point is that no additional regularity assumption on the state space and on the underlying transition semigroup is used.     

Very smooth points of spaces of operators

In this paper we study very smooth points of Banach spaces with special emphasis on spaces of operators. We show that when the space of compact operators is anM-ideal in the space of bounded operators, a very smooth operatorT attains its norm at a unique vectorx (up to a constant multiple) andT(x) is a very smooth point of the range space. We show that if for every equivalent norm on a Banach space, the dual unit ball has a very smooth point then the space has the Radon-Nikodym property. We give an example of a smooth Banach space without any very smooth points.     

On Commutators of Idempotents

It is shown that a pair of idempotent operators on a Banach space is triangularizable if their commutator is nilpotent. Moreover, if every operator on Hilbert space has an invariant subspace, then a pair of idempotents on Hilbert space is triangularizable if their commutator is quasinilpotent. These results are generalized from idempotents to quadratic operators.     

Geometric aspects of the moduli space of Riemann surfaces

We describe some recent progress in the study of moduli space of Riemann surfaces in this survey paper. New complete Kahler metrics were introduced on the moduli space and Teichmuller space. Their curvature properties and asymptotic behavior were studied in details. These natural metrics served as bridges to connect all the known canonical metrics, especially the Kahler-Einstein metric. We showed that all the known complete metrics on the moduli space are equivalent and have Poincare type growth. Furthermore, the Kahler-Einstein metric has strongly bounded geometry. This also implied that the logarithm cotangent bundle of the moduli space is stable in the sense of Mumford.     

Convergence of Riesz space martingales

We prove a martingale convergence for sub and super martingales on Riesz spaces. As a consequence we can form Krickeberg and Riesz like decompositions. The minimality of the Krickeberg decomposition yields a natural ordered lattice structure on the space of convergent martingales making this space into a Dedekind complete Riesz space. Finally we show that the Riesz space of convergent martingales is Riesz isomorphic to the order closure of the union of the ranges of the conditional expectations in the filtration. Consequently we can characterize the space of order convergent martingales both in Riesz spaces and in the setting of probability spaces.