可测空间与Pawlak代数

用可测集定义的上（下）方逼近算子apr(apr)讨论可测空间与Pawlak代数之间的关系,指出可测集即是明确集,可测空间（U,A）可扩张为（U,A）,使其满足任意并（交）的封闭性,从而将文献[1]的主要定理推广到一般情况。     

一类指数型整插值算子Holdr度量下的逼近和饱和

设S^Ua(f,x)=∑k∈Z(f(xk)Uσ(x-xk),xk=2kn/σ,k∈z,σ＞0,Uσ（y)=2/σ∫^σ0（Pi(σ－x))/P(ix) P(i(σ-x))cosxydx,其中P（t)=∑^mj=1是常数项为0的m次实系数多项式,m为奇数,本研究此指数型整插值算子在Holder度量下的近和饱和问题,确定了饱和类和饱和阶。     

线性算子σ（L^∞,L^1）逼近的Korovkin定理

本文给出并证明了拓扑σ（Ｌ＾∞，Ｌ＾１）下线性算子逼近Ｌ＾∞函数的Ｋｏｒｏｖｋｉｎ定理。     

本质正规三角算子模型的（u＋k）-轨道闭包

Hilbert空间H上有界线性算子T的（U＋K）-轨道定义为（U＋K）（T）={R^-1TR：R是作用在H上且具有酉算子＋紧算子表示形式的有界可逆算子}.本文刻画了满足H=∨{ker（T-λI）：λ∈ρF（T）}及σp（T^＊）=（？）的本质正规三角算子T的（U＋K）-轨道闭包,建立了具有三角算子、三角算子的伴随算子、正规算子直和形式的本质正规三角算子模型,并证明了如果这种算子模型具有相同的谱图象,则它们生成相同的（U＋K）-轨道闭包,同时也刻画了这种算子模型（U＋K）-轨道闭包.这些结果推广了本质正规算子（U＋K）-轨道闭包的有关已知结果,而且为Marcoux在＂A survey of（U＋K）-orbit＂中的问题2提出的公开猜想给出了更多肯定的情形.     

算子空间中秩一算子的稠密性

设u是Hilbert空间上的σ-弱闭算子空间,称u具有性质（P）,如果u中秩－算子生成的子空间在u中是σ－弱稠密的,称u具有扩张性质（P）,如果u以及包含u的每个σ－弱闭子空间都具有性质（P）,本文研究了性质（P）和扩张性质（P）,给出了它们的等从描述。     

重单值扩张算子的谱结构与拟相似

本文证明了,若T是重单值扩张算子,则若T1是重单值扩张（C）算子,T2是任一有界线性算子,T1与T2拟相似,则σe（T1）＝σk（T1）σk（T2）＝σe（T2）     

一类指数型整函数值算子的逼近性质

设（Ｕσｆ）（ｘ）＝Σ↓ｋ∈Ｚｆ（Ｘｋ）Ａσ（Ｘ－Ｘｋ），Ｘｋ＝２ｋπ／σ，ｋ∈Ｚ，σ〉０，ｆ是Ｒ上的有界函数，而Ａσ（ｙ）＝２／σ∫σ０ｓｉｎ＾ｍ（σ－Ｘ）ｈ／ｓｉｎ＾ｍ（σ－Ｘ）ｈ＋ｓｉｎ＾ｍｘｈｃｏｓｘｙｄｘ，ｍ为奇自然数，０〈ｈ〈π／σ，本文研究了此插值算子的收敛与饱和问题。     

W空间中最佳逼近插值算子

一元函数有种种不同的插值方法，如多项式插值，样条插值，有理插值等，也给出了最佳插值算子[2]本文对二元函数讨论最佳逼近插值算子．设X是点集Ω上的实函数空间，是Ω上给定的一组点．由下式确定x上的一组泛函设Xu是X的。维子空间，定义X到Xu的算子Hn：其中（a；闪丹ZCXn．对X的子集人称dA【VI“fill＿fillSlipwIVJ一【＊un八V川UJXnCX｛。。（Q）IVC。。irCh为A的逼近偏差．若某个n维子空IWXu达到（2）式的第一个下确界，则称此Xn为A的最佳逼近子空间，记为X：．X：中达到（2）式的第二个下确界的扣；（Q）｝Z称为A的最…     

良序套张量积的代数中的强不可约算子

设Ｈ为复的可分无限维Ｈｉｌｂｅｒｔ空间，称有界线性算子Ｔ为强不可约的，如果与Ｔ可交换的幂等算子只有０和Ｉ．王宗尧、蒋春澜、纪有清等人证明了在任何一个套的套代数中都存在大量的强不可约算子，并且找到了它们的酉轨道闭包．本文考虑有限个套的张量积的代数中强不可约算子的存在性问题。证明了：对复平面上任何一个连通完备集σ、总存在一个对角算子Ｎ和它的一个范数可以任意小的紧摄动Ｔ＝Ｘ＋Ｋ，使得Ｔ是一个强不可约算子、Ｔ在有限个良序套的张量积的代数中，并且σ（Ｔ）＝σｌｒｅ（Ｔ）＝σ（Ｎ）＝σｌｒｅ（Ｎ）＝σ进一步，文章还对具有单点谱的算子和良序套与正交补为良序套的张量积的代数进行了讨论，得到了一些结果．     

复合算子的次正常性

设（Ｓ，∑，μ）为一个σ－有限的测度空间，ｇ是从Ｓ到Ｓ使得复合算子Ｃｇ为有界算子的映射．本文证明了以下三个条件等价：１）Ｃｇ为Ｌ２（Ｓ，∑，μ）上的次正常算子；２）对所有自然数ｎ及几乎所有ｘ∈Ｓ，３）对几乎所有ｘ∈Ｓ，存在（０，‖Ｃｇ‖）上的概率测度μｘ使得     

A function space -compact space

Assuming that the minimal cardinality of a dominating family in is equal to , we construct a subset of a real line such that the space of continuous real-valued functions on does not admit any continuous bijection onto a -compact space. This gives a consistent answer to a question of Arhangel'skii.

     

Wasserstein space over the Wiener space

The goal of this paper is to study optimal transportation problems and gradient flows of probability measures on the Wiener space, based on and extending fundamental results of Feyel–Üstünel. Carrying out the program of Ambrosio–Gigli–Savaré, we present a complete characterization of the derivative processes for certain class of absolutely continuous curves. We prove existence of the gradient flow curves for the relative entropy w.r.t. the Wiener measure and identify these gradient flow curves with solutions of the Ornstein–Uhlenbeck evolution equation.     

The space of maps from a locally compact space to a Banach space

The space of continuous maps from a topological spaceX to topological spaceY is denoted byC(X,Y) with the compact-open topology. In this paper we prove thatC(X,Y) is an absolute retract ifX is a locally compact separable metric space andY a convex set in a Banach space. From the above fact we know thatC(X,Y) is homomorphic to Hilbert spacel ₂ ifX is a locally compact separable metric space andY a separable Banach space; in particular,C(R ⁿ,R^m) is homomorphic to Hilbert spacel ₂. This research is supported by the Science Foundation of Shanxi Province's Scientific Committee     

A rigid space homeomorphic to Hilbert space

A rigid space is a topological vector space whose endomorphisms are all simply scalar multiples of the identity map. This is in sharp contrast to the behavior of operators on , and so rigid spaces are, from the viewpoint of functional analysis, fundamentally different from Hilbert space. Nevertheless, we show in this paper that a rigid space can be constructed which is topologically homeomorphic to Hilbert space. We do this by demonstrating that the first complete rigid space can be modified slightly to be an AR-space (absolute retract), and thus by a theorem of Dobrowolski and Torunczyk is homeomorphic to .

     

Fock space on C∞ and Bose-Fock space

In this paper, we introduce the Fock space on ${\mathbb{C}}^{\infty }$ and obtain an isomorphism between the Fock space on ${\mathbb{C}}^{\infty }$ and Bose-Fock space. Based on this isomorphism, we obtain representations of some operators on the Bose-Fock space and answer a question in [2]. As a physical application, we study the Gibbs state.     

A characterization of Bloch space and Besov space

On the unit disk of the complex plane, a characterization for the membership of Bloch space and analytic Besov space is expressed extending known results.     

A metric space of directions in Minkowski space

A new angular measure in a d-dimensional Minkowski space M was introduced recently. It determines the lengths of rectifiable curves in the (d - 1)-dimensional topological sphere S of all directions in M. Thus, a length structure appears on S. This results in the appropriate intrinsic metric in S. The paper deals with some properties of the length structure and the resulting metric space S. In particular, it shows that diam S 2 .     

Hardy space and Bergman space on the Octonions

In this paper, square-integrable Octonion-valued function spaces on R³ and R⁷ are decomposed into the direct sum of Octonion Hardy and conjugate Hardy spaces, and square-integrable Octonion function spaces on the upper half spaces R ₊ ⁴ and R ₊ ⁸ are decomposed into infinity direct sum of subspaces in which the first components are just the Octonion Bergman spaces. The Octonion Hardy Spaces on R³ and R⁷ are characterized.     

Hardy空间到加权Hardy空间上的复合算子

本文研究了从Hardy空间到加权Hardy空间上的复合算子,并给出此复合算子为有界和紧的条件。