Teichmüller Spaces and Function Spaces

ＴｅｉｃｈｍüｌｅｒＳｐａｃｅｓａｎｄＦｕｎｃｔｉｏｎＳｐａｃｅｓＧｕｏＨｕｉ（郭辉）（ＳｃｈｏｌｏｆＭａｔｈｅｍａｔｉｃａｌＳｃｉｅｎｃｅ，ＰｅｋｉｎｇＵｎｉｖｅｒｓｉｔｙ，Ｂｅｉｊｉｎｇ，１００８７１）ＣｏｍｍｕｎｉｃａｔｅｄｂｙＬｉＺｈｏｎｇＲ...     

Fuzzy S-Regular Spaces and S-Almost Regular Spaces

ＦｕｚｚｙＳＲｅｇｕｌａｒＳｐａｃｅｓａｎｄＳＡｌｍｏｓｔＲｅｇｕｌａｒＳｐａｃｅｓＦａｎｇＪｉｎｍｉｎｇ（ＤｅｐａｒｔｍｅｎｔｏｆＡｐｐｌｉｅｄＭａｔｈｅｍａｔｉｃｓ，ＯｃｅａｎＵｎｉｖｅｒｓｉｔｙｏｆＱｉｎｇｄａｏ，Ｑｉｎｇｄａｏ，２６６０...     

γ-Compact Spaces

Let X be a topological space, denote iA and cA the interior and the closure of A ⊂ X, respectively, and let γ = c o i, or = i o c, or = i o c o i, or = c o i o c. A set A ⊂ X is said to be γ-open [5] iff A ⊂ γ(A). The space X is γ-compact iff each cover of X composed of γ-open sets admits a finite subcover. The purpose of the paper is to investigate some questions concerning γ-compact and related spaces. This revised version was published online in June 2006 with corrections to the Cover Date.     

Variable Besov-type Spaces

In this paper we introduce Besov-type spaces with variable smoothness and integrability.We show that these spaces are characterized by the φ-transforms in appropriate sequence spaces and we obtain atomic decompositions for these spaces.Moreover the Sobolev embeddings for these function spaces are obtained.     

Toric Rigid Spaces

This paper gives a method to construct rigid spaces, which is similar to the method used to construct toric schemes.     

On P-sober Spaces

In this paper,we focus on p-sober spaces and prove that(1) the To space X is p-sober if and only if the Smyth power space of X is p-sober;(2) the space X has a p-sober dcpo model if and only if X is T₁ and p-sober;(3) every non-p-sober T₀ space does not have a p-sobrification;(4) the T₀ space X is sober if and only if X is p-sober and PD.     

Very Convex Banach Spaces

ＶｅｒｙＣｏｎｖｅｘＢａｎａｃｈＳｐａｃｅｓＴｅｇｕｓｉ（特古斯）Ｓｕｙａｌａｔｕ（苏雅拉图）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＩｎｎｅｒＭｏｎｇｏｌｉａＮｏｒｍａｌＵｎｉｖｅｒｓｉｔｙ，Ｈｕｈｈｏｔ，０１００２２）ＬｉＹｏｎｇｊｉｎ...     

Embedding of Möbius Invariant Function Spaces into Tent Spaces

On the unit disk we introduce a new class of tent spaces \(T^q_{s,t}(\mu )\) for any positive Borel measure \(\mu \), consider a class of Möbius invariant spaces \(Z_p\) of analytic functions, and show that \(Z_p\) is contained in \(T^1_{p,1}\) if and only if \(\mu \) is a p-Carleson measure. This could be considered a continuation or variation of the work initiated by Xiao (Adv Math 217:2075–2088, 2008).     

Amarts on Riesz Spaces

The concepts of conditional expectations, martingales and stopping times were extended to the Riesz space context by Kuo, Labuschagne and Watson （Discrete time stochastic processes on Riesz spaces, Indag. Math.,15（2004）, 435-451）. Here we extend the definition of an asymptotic martingale （amart） to the Riesz spaces context, and prove that Riesz space amarts can be decomposed into the sum of a martingale and an adapted sequence convergent to zero. Consequently an amart convergence theorem is deduced.     

Regular Spaces and Hyper-spaces

We are concerned with the construction of regular spaces and hyper-spaces,and the characterization of continuous linear operators in such spaces.     

On k-Strictly Convex and k-Very Smooth Banach Spaces

Ｏｎｋ－ＳｔｒｉｃｔｌｙＣｏｎｖｅｘａｎｄｋ－ＶｅｒｙＳｍｏｏｔｈＢａｎａｃｈＳｐａｃｅｓＺｈａｎｇＺｉｈｏｕ（张子厚）（ＨｕａｉｎａｎＴｅｌｅｃｉｓｉｏｎＵｎｉｖｅｒｓｉｔｙ,Ｈｕａｉｎａｎ,Ａｎｈｕｉ,２３２００１）Ａｂｓｔｒａｃｔ：Ｉｎｔｈｉｓ...     

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.     

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.     

弱^＊局部一致凸空间的一些性质

讨论了弱^*局部一致凸空间的一些等价定义和性质,以及乘积空间的弱^*凸部一致凸的传递性。     

相对积空间的Os-连通性

研究L-拓扑空间的相对乘积空间的Os-连通性。     

L-拓扑空间相对积空间的s-连通性

证明了s-连通性关于相对乘积运算是可乘的且是L-好推广。     

闭模糊拟阵的特征

给出Goetchel和Voxman定义的模糊拟阵成为闭模糊拟阵的三个充分必要条件。     

模糊粗糙线性空间

将粗糙集理论引入到线性空间与模糊线性空间中,分别给出了上粗与下粗线性空间及模糊上粗与模糊下粗线性空间的概念,并研究了它们的有关性质,获得了一系列有意义的结果。     

MV-代数的素滤子MV-拓扑空间

在MV-方体[0,1]X的子集Ω上引进MV-拓扑结构,并套论MV-拓扑空间的紧性、Hausdorff分离性等拓扑性质.细致地讨论MV-代数的素滤子集上的MV-拓扑空间(M,ΩM),证明素滤子MV-拓扑空间是紧Hausdorff MV-空间,并且它还是良紧空间.作为应用,证明一个σ-完备格M是MV-代数当且仅当M同构于某个Stone MV-空间的MV-开闭集格.