保谱乘法映射

设X,Y为Banach空间,证明了B（X）到B（Y）的保谱乘法满射φ具有形式φ（T）＝ATA-1,其中A为X到Y上的同构．     

基序列与有界线性算子

该文用基序列来刻划Banach空间的几何性质，以及Banach空间中某些特殊算子的特征，得到一些好的结果．如有界线性算子T：X→Y是一个同构的充分必要条件是T在X的每个具有基的子空间上的限制也是一个同构．对紧算子T：c0→X也有众多的刻划．     

保持谱半径的乘法映射

设X和Y为无限维Banach空间,Φ：B（X）→B（Y）是保持谱半径的满射,且秩为1算子,则Φ具有形式Φ（T）=ATA∧-1,这里A：X→Y或是线性拓扑同构映射或是线性拓扑同构映射的共轭。     

Banach空间中线性算子的(集值)度量广义逆的表示及应用

在Banach空间Y无自反和从Banach空间X到Y的线性算子T无闭值域和稠定的假定下,利用Banach空间几何方法证明了Banach空间中线性算子的度量广义逆是具有闭凸值的集值映射,建立了该度量广义逆的存在性、唯一性和等价表达式,并给出了此表达式的一个应用示例．所得的部分结果本质地拓广王玉文和潘少荣在Banach空间Y自反,从X到Y的线性算子T为闭值域和稠定的假定下的近期相应结果．     

Banach空间中线性流形的单值度量投影算子部分

为了研究Banach空间集值线性映射包含y∈M(x)的最小范数极值解,其中X,Y为Banach空间,M X×Y为线性流形,本文引入Banach空间X×Y中线性流形的单值度量算子部分,并给出了该算子部分的结构的刻划.为在另文将Lee S J与NashedM Z所引进并研究的Hilbert空间中集值线性映射包含的最小二乘解推广到Banach空间奠定了理论基础.     

正则余弦算子函数的内插和外插定理

该文研究正则余弦算子函数的内插和外插．证明了线性算子A在Banach空间X中生成一个指数有界的C-正则余弦函数当且仅当存在Banach空间Y和线性算子B使得：［R这里是C在Y中的有界扩张，B在Y中生成一个强连续余弦算子函数且A＝B|x．     

二阶导数条件下带参数的修正型Halley迭代族的局部收敛性北大核心CSCD

1 引言 设X和Y为实的或复的Banach空间,Ω X是开凸子集,F：Ω X→y是二阶连续可微的非线性算子．非线性算子方程F（x）=0．     

lp(1≤p<∞)商空间的Maluta常数

为研究介于正规结构和一致正规结构之间的Banach空间的结构性质，Maluta[1]给出Banach空间X的Maluta常数D（X）的定义，该文给出当M是X的具Schur性的可余闭子空间时有D（X／M）＝D（X），并计算出lp商空间的Maluta常数．     

Banach代数L∞(T;X)

讨论向量值函数的Banach代数L∞（T；X）的极大理想空间的拓扑性质和代数性质，得到了若干结果；给出了Banach空间H∞（D；X）中闭单位球的端点的一条性质．     

Banach空间上的左可逆算子的稳定性

主要讨论了Banach空间上左可逆算子在线性运算上的稳定性及一些摄动问题，并通过反例证明了对于Banach空间上的左可逆算子A和B，R（A）∩R（B）＝{0}不是λA＋B（λ∈C）为左可逆算子的必要条件。     

A new characterization of dual bases in finite fields and its applications

We propose a new characterization of dual bases in finite fields. Let A=(α₁,…,α_n) be a basis of F over F_q and its dual basis B=(β₁,…,β_n) with the transition matrix C∈GL_n(F_q) such that (β₁,…,β_n)=(α₁,…,α_n)C. We show that holds for all 1?k?n, where T_k∈M_n(F_q) satisfies α_k(α₁,…,α_n)=(α₁,…,α_n)T_k. Conversely, suppose F=F_q(α_k^′) and for some 1?k^′?n and G∈GL_n(F_q), then B is equivalent to (α₁,…,α_n)G. As applications, we can construct the dual basis of a given basis A or determine whether the dual basis of A satisfies the desired conditions from T_k. This generalizes the results obtained by Liao and Sun for normal bases. Furthermore, we give a simple proof of the theorem of Gollmann, Wang and Blake for polynomial bases.     

On the Restricted Order of Asymptotic Bases of Order Two

The restricted order of an asymptotic basis A is the least integer h, if it exists, such that every sufficiently large integer is the sum of h or fewer distinct elements of A. We show that any asymptotic basis of order 2 has a restricted order at most equal to 4. We also provide an example of an additive basis of order 2 whose restricted order is 4.To Jean-Louis Nicolas2000 Mathematics Subject Classification: Primary—11B13     

Characterizations of multi-knot piecewise linear spectral sequences

We study two classes of orthonormal bases for in this paper. The exponential parts of these bases are multi-knot piecewise linear functions. These bases are called spectral sequences. Characterizations of these multi-knot piecewise linear functions are provided. We also consider an opposite problem for single-knot piecewise linear spectral sequences, where the piecewise linear functions are defined on and . We show that such spectral sequences do not exist except for . *Supported by the Technology and Research project 2002YF015 of the Ministry of Railway of China and by the Natural Science Foundation of China under grant 10371122. **Supported by the Presidential Foundation of Graduate School of the Chinese Academy of Sciences (yzjj200505).     

A representation theorem for Schauder bases in Hilbert space

A sequence of vectors in a separable Hilbert space is said to be a Schauder basis for if every element has a unique norm-convergent expansion

If, in addition, there exist positive constants and such that

then we call a Riesz basis. In the first half of this paper, we show that every Schauder basis for can be obtained from an orthonormal basis by means of a (possibly unbounded) one-to-one positive self adjoint operator. In the second half, we use this result to extend and clarify a remarkable theorem due to Duffin and Eachus characterizing the class of Riesz bases in Hilbert space.

     

An example of an almost greedy uniformly bounded orthonormal basis for

We construct a uniformly bounded orthonormal almost greedy basis for L_p(0,1), 1<p<∞. The example shows that it is not possible to extend Orlicz's theorem, stating that there are no uniformly bounded orthonormal unconditional bases for L_p(0,1), p≠2, to the class of almost greedy bases.     

The Basis Number of Some Special Non-Planar Graphs

The basis number of a graph G was defined by Schmeichel to be the least integer h such that G has an h-fold basis for its cycle space. He proved that for m, n 5, the basis number b(K _m,n ) of the complete bipartite graph K _m,n is equal to 4 except for K _6,10, K _5,n and K _6,n with n = 5, 6, 7, 8. We determine the basis number of some particular non-planar graphs such as K _5,n and K _6,n , n = 5, 6, 7, 8, and r-cages for r = 5, 6, 7, 8, and the Robertson graph.     

Minimal and maximal unconditional bases with respect to framings

This paper studies framings in Banach spaces, a concept raised by Casazza, Han and Larson, which is a natural generalization of traditional frames in Hilbert spaces and unconditional bases in Banach spaces. The minimal unconditional bases and the maximal unconditional bases with respect to framings are introduced. Our main result states that, if （xi, fi） is a framing of a Banach space X, and （eimin） and （eimax） are the minimal unconditional basis and the maximal unconditional basis with respect to （xi, fi）, respectively, then for any unconditional basis （ei） associated with （xi, fi）, there are A,B 〉 0 such that A｜｜i=1∑∞aieimin｜｜≤｜｜i=1∑∞aiei｜｜≤B｜｜i=1∑∞aieimax｜｜ for all （ai） ∈ c00.
It means that for any framing, the corresponding associated unconditional bases have common upper and lower bounds.     

Some decision and counting problems of the Duquenne-Guigues basis of implications

Implications of a formal context obey Armstrong rules, which allows one to define a minimal (in the number of implications) implication basis, called Duquenne-Guigues basis or stem base in the literature. In this paper we show how implications are reduced to functional dependencies and prove that the problem of determining the size of the stem base is a #P-complete problem.     

The Dual Functionals for the Generalized Ball Basis of Wang-Said Type and Basis Transformation Formulas

The generalized Ball curves of Wang-Said type with a position parameter L not only unify the Wang-Ball curves and the Said-Ball curves, but also include several useful intermediate curves. This paper presents the dual functionals for the generalized Ball basis of Wang-Said type. The relevant basis transformation formulae are also worked out.     

Orthonormal bases associated with multi-knot piecewise linear function sequences on [0, 1)<Superscript><Emphasis Type="Italic">n</Emphasis></Superscript>

We investigate two classes of orthonormal bases for L^2（[0, 1）^n）. The exponential parts of those bases are multi-knot piecewise linear functions which are called spectral sequences. We characterize the multi-knot piecewise linear spectral sequences and give an application of the first class of piecewise linear spectral sequences.