A New Class of Banach Spaces with Uniform Normal Structure

§ 1.Ｉｎｔｒｏｄｕｃｔｉｏｎ　ＬｅｔＸｂｅａｎｏｒｍｅｄｌｉｎｅａｒｓｐａｃｅ ,ａｎｄｌｅｔＳ(Ｘ) ={ｘ∈Ｘ :ｘ =1 }ｂｅｔｈｅｕｎｉｔｓｐｈｅｒｅｏｆＸ .Ｉｎ 1 94 8,ＢｒｏｄｓｋｉｉａｎｄＭｉｌｍａｎ[1]ｉｎｔｒｏｄｕｃｅｄｔｈｅｆｏｌｌｏｗｉｎｇｇｅｏｍｅｔｒｉｃｃｏｎｃｅｐｔ:　Ｄｅｆｉｎｉｔｉｏｎ 1　ＡＢｏｕｎｄｅｄ ,ｃｏｎｖｅｘｓｕｂｓｅｔＫｏｆａＢａｎａｃｈｓｐａｃｅＸｉｓｓａｉｄｔｏｈａｖｅｎｏｒｍａｌｓｔｒｕｃｔｕｒｅｉｆｅｖｅｒｙｃｏｎｖｅｘｓｕｂｓｅｔＨｏｆＫｔｈａｔｃｏｎｔａ…     

The Compact Characterhations of the Operator H_fH_g on the Bergman Space

ＴｈｅＣｏｍｐａｃｔＣｈａｒａｃｔｅｒｈａｔｉｏｎｓｏｆｔｈｅＯｐｅｒａｔｏｒＨ＿ｆＨ＿ｇｏｎｔｈｅＢｅｒｇｍａｎＳｐａｃｅＧｕｏＫｕｎｙｕ（郭坤宇)（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＳｉｃｈｕａｎＵｎｉｖｅｒｓｉｔｙ，Ｃｈｅｎｇｄｕ?..     

Two Questions on Local Properties

ＬｅｔＸｂｅａｓｐａｃｅ ,ａｎｄＱａｔｏｐｏｌｏｇｉｃａｌｐｒｏｐｅｒｔｙ .Ｉｆｆｏｒｅａｃｈｘ∈Ｘ ,ｔｈｅｒｅｅｘｉｓｔｓａｎｅｉｇｈｂｏｒｈｏｏｄＵｏｆｘｓｕｃｈｔｈａｔＵｈａｓｐｒｏｐｅｒｔｙＱ ,ｔｈｅｎｗｅｃａｌｌＸａｌｏｃａｌＱ ｓｐａｃｅ .　Ｄｅｆｉｎｉｔｉｏｎ 1　ＡｓｐａｃｅＸｉｓｃａｌｌｅｄθ ｒｅｆｉｎａｂｌｅ,ｉｆｆｏｒｅｖｅｒｙｏｐｅｎｃｏｖｅｒＵｏｆＸｔｈｅｒｅｅｘｉｓｔｓａｓｅｑｕｅｎｃｅ {Ｕｎ}ｏｆｏｐｅｎｒｅｆｉｎｅｍｅｎｔｓｏｆＵｓｕｃｈｔｈａｔｆｏｒｅａｃｈｘ∈Ｘ ,…     

Coupled Quasisolutions of Volterra Intergral Equations with Discontinuons Terms in Banach Spaces

ＣｏｕｐｌｅｄＱｕａｓｉｓｏｌｕｔｉｏｎｓｏｆＶｏｌｔｅｒｒａＩｎｔｅｒｇｒａｌＥｑｕａｔｉｏｎｓｗｉｔｈＤｉｓｃｏｎｔｉｎｕｏｎｓＴｅｒｍｓｉｎＢａｎａｃｈＳｐａｃｅｓ￥ＺｈｏｕＺｈｉ；（周智）ＹｕＺｈａｏｘｉａ（于朝霞）（ＳｈａｎｄｏｎｇＩｎｓｔ...     

On the Order of Best Approximation by Polynomials in H_q~p Spaces

ＯｎｔｈｅＯｒｄｅｒｏｆＢｅｓｔＡｐｐｒｏｘｉｍａｔｉｏｎｂｙＰｏｌｙｎｏｍｉａｌｓｉｎＨ■ＳｐａｃｅｓＸｉｎｇＦｕｃｈｏｎｇ（邢富冲）（ＣｅｎｔｒａｌＵｎｉｖｅｒｓｉｔｙｆｏｒＮａｔｉｏｎａｌｉｔｉｅｓ，Ｂｅｉｊｉｎｇ，１０００８１）Ｃｏｍｍｕｎｉ...     

On Local Integrated Cosine Functions

§ 1.Ｉｎｔｒｏｄｕｃｔｉｏｎ　Ｔｈｒｏｕｇｈｏｕｔｔｈｉｓｐａｐｅｒ,ＸｉｓａＢａｎａｃｈｓｐａｃｅ,ｅｑｕｉｐｐｅｄｗｉｔｈａｎｏｒｍ· ,Ｂ(Ｘ)ｓｔａｎｄｓｆｏｒｔｈｅＢａｎａｃｈａｌｇｅｂｒａｏｆａｌｌｂｏｕｎｄｅｄｌｉｎｅａｒｏｐｅｒａｔｏｒｓｏｎＸ ,Ｂ(Ｘ ,Ｙ)ｆｏｒｔｈｅｓｅｔｏｆｂｏｕｎｄｅｄｌｉｎｅａｒｏｐｅｒａｔｏｒｓｆｒｏｍＸｔｏａｎｏｔｈｅｒＢａｎａｃｈｓｐａｃｅＹ ,ＡｆｏｒａｃｌｏｓｅｄｏｐｅｒａｔｏｒｏｎＸ ,ρ(Ａ)ｆｏｒｔｈｅｒｅｓｏｌｖｅｎｔｓｅｔｏｆＡ ,Ｄ(Ａ)ｆｏｒｔｈ…     

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

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

Inverse Limit of Spaces of Upper Semicontinuous Functions

ＳｕｐｐｏｓｅｔｈａｔＸｉｓａｃｏｍｐａｃｔＨａｕｓｄｏｒｆｆｓｐａｃｅ,ａｎｄＵ(Ｘ)ｄｅｎｏｔｅｓｔｈｅｓｅｔｏｆａｌｌｔｈｅｕｐｐｅｒｓｅｍｉｃｏｎｔｉｎｕｏｕｓｆｕｎｃｔｉｏｎｓｆｒｏｍＸｔｏ [0 ,1 ] .ＴｈｅｎＵ(Ｘ)ｉｓａｃｏｍｐｌｅｔｅｌａｔｔｉｃｅｕｎｄｅｒｔｈｅｐｏｉｎｔｗｉｓｅｏｒｄｅｒｉｎｇ ,ａｎｄｉｔｓｏｐｐｏｓｉｔｅｌａｔｔｉｃｅＵ(Ｘ) ｏｐｉｓａｃｏｎｔｉｎｕｏｕｓｌａｔｔｉｃｅ .ＴｈｕｓＵ(Ｘ)ｅｎｄｏｗｅｄｗｉｔｈｔｈｅｌｉｍ ｉｎｆｔｏｐｏｌｏｇｙｏｎＵ(Ｘ) ｏｐ,ｗｈｉｃ…     

Toeplitz Algebras on Dirichlet Spaces

§ 1.Ｉｎｔｒｏｄｕｃｔｉｏｎ　ＬｅｔＢｎｂｅｔｈｅｕｎｉｔｂａｌｌｉｎＣｎ,ａｎｄｄｖｔｈｅｎｏｒｍａｌｉｚｅｄＬｅｂｅｓｇｕｅｍｅａｓｕｒｅｏｎＢｎ.ＳｏｂｏｌｅｖｓｐａｃｅＬ2 ,1ｉｓｔｈｅｓｐａｃｅｏｆｆｕｎｃｔｉｏｎｓｕ :Ｂｎ→Ｃ ,ｆｏｒｗｈｉｃｈｔｈｅｎｏｒｍ‖ｕ‖1/ 2 =∑ｎｉ=1 ∫Ｂｎ ｕ ｚｉ(ｚ) 2 + ｕ ｚｉ(ｚ) 2 ｄν1/ 2 <∞ .Ｌ2 ,1/ 2 ｉｓａＨｉｌｂｅｒｔｓｐａｃｅｗｉｔｈｔｈｅｉｎｎｅｒｐｒｏｄｕｃｔ〈ｕ ,ｖ〉1/ 2 =∑ｎｉ=1〈 ｕ ｚｉ, ｕ ｚｉ〉Ｌ2 (ｄν) +∑ｎｉ=1〈 ｕ ｚｉ, ｕ …     

ANoteonWeaklyCompactSetsinBanachSpace

ＡＮｏｔｅｏｎＷｅａｋｌｙＣｏｍｐａｃｔＳｅｔｓｉｎＢａｎａｃｈＳｐａｃｅ＊）ＷａｎｇＸｉａｏｍｉｎ＊＊）（王晓敏）（ＤｅｐａｒｔｍｅｎｔｏｆＭａｔｈｅｍａｔｉｃｓ，ＨａｒｂｉｎＩｎｓｔｉｔｕｔｅｏｆＴｅｃｈｎｏｌｏｇｙ，Ｈａｒｂｉｎ，１５０００１）...     

Hilbert空间中耗散算子的性质研究

文章研究了Hilbert空间中耗散算子的性质,并给出此类算子成为C0压缩半群无穷小生成元的一些条件。     

Orders in rings without identity

G. Lallement [5] proved that every idem potent congruence class of a regular semigroup contains an idem potent. P. Edwards [4] generalized this property of congruences to eventually regular semigroups. Using the natural partial order of the semigroup (see [6]) a weakened version of this result will be proved for the more general class of E-inversive semigroups. But for particular congruences the original result of Lallement still holds for every E-inversive semigroup. Finally, conditions for a congruence on a general semigroup (with E(S) a subsemigroup, resp.) are given, which ensure that Lallement's result holds.     

Semigroups of right quotients of a semigroup which is a semilattice of groups

Let S be a semigroup with zero which is a semilattice of groups. In [6], McMorris showed that the semigroup of quotients Q=Q(S) corresponding to the filter of “dense” right ideals of the semigroup S is also a semilattice of groups. He accomplished this by noting that Q is a regular semigroup in which all idempotents are central, an equivalent formulation of a semilattice of groups. In this paper we develop the semigroup of quotients Q corresponding to an arbitrary right quotient filter on S (as defined herein) and note the above result in this more general setting by explicitly constructing a semigroup which is isomorphic to Q. We also see that the underlying semilattice for Q in this case is isomorphic to a semigroup of quotients of the original semilattice for the semigroup S.     

Transport equation in unbounded slab geometry: asymptotic behavior

In this work we are concerned with the one-dimensional transport equation, on unbounded slab, endowed with a general boundary condition. We show that this equation is governed by a strongly continuous semigroup. We investigate the spectral and lattice properties of the generated semigroup and prove the existence of a leading eigenvalue with algebraic multiplicity one. We end this work by describing the asymptotic behavior of the generated semigroup in the uniform topology.     

A novel dual approach to nonlinear semigroups of Lipschitz operators

Lipschitzian semigroup refers to a one-parameter semigroup of Lipschitz operators that is strongly continuous in the parameter. It contains -semigroup, nonlinear semigroup of contractions and uniformly -Lipschitzian semigroup as special cases. In this paper, through developing a series of Lipschitz dual notions, we establish an analysis approach to Lipschitzian semigroup. It is mainly proved that a (nonlinear) Lipschitzian semigroup can be isometrically embedded into a certain -semigroup. As application results, two representation formulas of Lipschitzian semigroup are established, and many asymptotic properties of -semigroup are generalized to Lipschitzian semigroup.

     

椭圆型算子的扩张及■半群

<正> 如何构造一个马尔科夫过程以G为生成元素(在适当的定义域上)的问题,在[1a]中已经给出回答.[1a]中假定系数a_(ij)(x),b_j(x),c(x)皆有界.可以证明在此条件下,过程的极限分布必为零;当l>2时,对应的过程必为非常返的(定义见[2]).这种限制把最典     

CHARACTERISTIC CONDITIONS FOR THECOMPLETE INFINITESIMAL GENERATORS OFANALYTIC SEMIGROUPS OF GROWTH ORDER α

1IntroductionandMainResultLetXbeacomPlexBanachspaceandletB(X)bethesetofaJlboundedlinearoperatorsfromXintoitselLAccordingtoDaPratol1],Sobole.skii[4]andZafievskii[6],aoneparameter~ly{T(t);t>o}CB(X)iscalledasemigroupofgrowtl1ordercr>Oif(Al)T(t s)=T(t)T(s)fort,s>oandT(t)xiscolltinuousillt>oforeachxEX;(Az)IfT(t)z=oforallt>O,thenx=o;(As)Ilt"T(t)IIisboundedast-O ;(A4)Xo=U,>.T(t)XisdenseinX.TheinfinitesimalgeneratorAoof{T(t);t>o}isdefinedbyItisknown[2]thatAoisclosable.LetA=Ao,thenA…     

关于非线性Lipschitz算子半群生成元的存在性

基于作者先前提出的Lipschitz对偶思想,对非线性Lipschitz算子半群引入了若干Lipschitz对偶概念,得到了一类非线性Lipschitz算子半群存在生成元的特征刻画.这一结果直接将关于C0-半群如下结论推广到了非线性情形:C0-半群具有有界生成元当且仅当它一致连续.     

Bipartite graphs and completely 0-simple semigroups

In a manner similar to the construction of the fundamental group of a connected graph, this article introduces the construction of a fundamental semigroup associated with a bipartite graph. This semigroup is a 0-direct union of idempotent generated completely 0-simple semigroups. The maximal nonzero subgroups are the corresponding fundamental groups of the connected components. Adding labelled edges to the graph leads to a more general completely 0-simple semigroup. The basic properties of such semigroups are examined and they are shown to have certain universal properties as illustrated by the fact that the free completely simple semigroup on n generators and its idempotent generated subsemigroup appear as special cases.     

Filters in (Quasiordered) Semigroups and Lattices of Filters

A filter in a semigroup is a subsemigroup whose complement is an ideal. (Alternatively, in a quasiordered semigroup, a slightly more general definition can be given.) We prove a number of results related to filters in a semigroup and the lattice of filters of a semigroup. For instance, we prove that every complete algebraic lattice can be the lattice of filters of a semigroup. We prove that every finite semigroup is a homomorphic image of a finite semigroup whose lattice of filters is boolean and which belongs to the pseudovariety generated by the original semigroup. We describe filter lattices of some well-known semigroups such as full transformation semigroups of finite sets (which are three-element chains) and free semigroups (which are boolean).