Matrix Transformations of the Maddox Vector-Valued Sequence Spaces

In this paper, we give the matrix characterizations from any normal vector-valued FK-space containing ø(X) into scalar-valued sequence space c(q) and by applying this result, we also obtain necessary and sufficient conditions for infinite matrices mapping the sequence spaces , and F_r(X,p) into the space c(q), where p = (p_k) and q = (q_k) are bounded sequences of positive real numbers and r ≥ 0.AMS Subject Classification (2000): 46A45.     

Matrix Transformations of the Maddox Vector-Valued Sequence Spaces

In this paper, we give the matrix characterizations from any normal vector-valued FK-space containing ø(X) into scalar-valued sequence space c(q) and by applying this result, we also obtain necessary and sufficient conditions for infinite matrices mapping the sequence spaces , and F_r(X, p) into the space c(q), where p = (Pk) and q = (qk) are bounded sequences of positive real numbers and r 0.AMS Subject Classification (2000): 46A45.     

The Dual Spaces of Sets of Difference Sequences of Order <Emphasis Type="Italic">m</Emphasis> and Matrix Transformations

Let p = （pk）k=0^∞ be a bounded sequence of positive reals, m C N and u be s sequence of nonzero terms. If x = （xk）k=0^∞ is any sequence of complex numbers we write Δ（m）x for the sequence of the m th order differences of x and Δu^（m）X = {x=（x）k=0^∞ uΔ（m）x ∈ X} for any set X of sequences. We determine the α-, β- and γ-duals of the sets Δμ^（m）X for X=co（p）,c（p）,l∞（p） and characterize some matrix transformations between these spaces Δ^（m）X.     

On Conservative Matrix Methods for Double Sequence Spaces

We consider two types of summability methods of double sequences defined by 4-dimensional matrices. Our concern is with methods preserving the regular convergence (in Hardy"s sense) and the -convergence of double sequences defined as follows: every column is convergent and the sequence of column limits converges as well. Of primary interest is whether the following well-known facts of summability concerning the summation of bounded sequences by conservative matrices can be extended to 4-dimensional matrices: (1) if the space of all convergent sequences is closed in a summability domain then the matrix does not sum bounded divergent sequences, (2) if a conservative matrix sums a divergent sequence then it sums an unbounded sequence and (3) two regular matrices are consistent on bounded sequences. We emphasize that the negative answer to (2), in the case of regular convergence, shows that the main result in [8] fails in general.     

Atomic Decompositions for Two-Parameter Vector-Valued Martingales and Two-parameter Vector-valued Martingale Spaces

In this paper atomic decompositions for two-parameter vector-valued martingales are given. With the help of the atomic decompositions the relations between the mutual embedding of two-parameter vector-valued martingale spaces and geometric properties of Banach spaces are investigated. Our study shows that geometric properties of Banach spaces determine the embedding of martingale spaces and conversely the latter can characterize the former. This revised version was published online in June 2006 with corrections to the Cover Date.     

向量值哈代-洛伦茨空间

对于1r∞与巴拿哈空间B=L~r(Ω,F,μ),我们研究了欧几里得空间R~n上B-值缓分布构成的哈代-洛伦茨空间H~(p,q)(R~n,B)及哈代-洛伦茨空间之间的内插,其中0p∞和0q≤∞,获得了H~(p,q)(R~n,B)的一系列等价的刻画及其原子分解.若Ω={1},则H~(p,q)(R~n,B)=H~(p,q)(R~n)是经典的情形;若Ω=Z是整数集且μ是Z上的计数测度并且r=2,0p∞及q=∞,则H~(p,q)(R~n,B)=H~(p,∞)(R~n,e~2)转化为Grafakos和He在文[Weak Hardy spaces,Preprint,2014]中讨论的情形.     

枢轴消去变换的若干性质

得到了与Gauss消去变换有着密切联系的枢轴消去变换的三个重要性质.     

Orthogonality Preserving Transformations on Indefinite Inner Product Spaces: Generalization of Uhlhorn's Version of Wigner's Theorem

We present an analogue of Uhlhorn's version of Wigner's theorem on symmetry transformations for the case of indefinite inner product spaces. This significantly generalizes a result of Van den Broek. The proof is based on our main theorem, which describes the form of all bijective transformations on the set of all rank-one idempotents of a Banach space which preserve zero products in both directions.     

关于Orlicz序列空间的包含关系

设Φ,Ψ为一对互余的Ｎ－函数,本文给出了包含关系成立的充要条件,并修正Ｃｈｅｎ［１,ｐ,１６８］的一个例子.     

On Some New Generalized Difference Sequence Spaces

Let (x) = A(x) , where A(x) denotes the number of square-full integers not exceeding x. In this paper, we prove that (x) = O , which improves the exponent 4/27 obtained by Y.-C. Cai [5].     

多重向量值正交小波包

本文引入多重向量值小波包的概念,提供一类多重向量值正交小波包的构造方法,并运用积分变换和算子理论,讨论了多重向量值正交小波包的性质．利用多重向量值正交小波包,构造了空间L2(R,Cs×s)的新的正交基．     

Preduals of Spaces of Vector-Valued Holomorphic Functions

For U a balanced open subset of a Fréchet space E and F a dual-Banach space we introduce the topology on the space of holomorphic functions from U into F. This topology allows us to construct a predual for which in turn allows us to investigate the topological structure of spaces of vector-valued holomorphic functions. In particular, we are able to give necessary and sufficient conditions for the equivalence and compatibility of various topologies on spaces of vector-valued holomorphic functions.     

多尺度多重向量值双正交小波的构建算法与性质

研究多尺度多重向量值双正交小波的构建算法与性质.运用向量细分格式、矩阵理论和多重向量值多分辨分析,证明了与一对给定的多尺度多重向量值双正交尺度函数对应的多尺度多重向量值双正交小波函数的存在性.提出了紧支撑多尺度多重向量值双正交小波的构造算法.讨论了多尺度多重向量值小波包的性质,得到了多重向量值小波包的双正交公式与向量值小波包基.     

Entropy Numbers of Diagonal Operators between Vector-Valued Sequence Spaces

Upper and lower bounds are established for the entropy numbersof certain diagonal operators between Banach sequence spaces.These diagonal operators are isomorphisms between the spacesconsidered in the paper and weighted sequence spaces consideredby Leopold so that the entropy numbers in question coincidewith those considered by Leopold. The results in the paper improvethe previous results in at least two ways. The estimates inthe paper are ‘almost’ sharp in the sense that theupper and lower estimates differ only by logarithmic factorsfor a much wider range of parameters. Moreover, all the upperestimates are improvements on the previous ones, the improvementbeing quite significant in some cases.     

Barrelledness of Generalized Sums of Normed Spaces

Let (E _i ) _iI be a family of normed spaces and a space of scalar generalized sequences. The -sum of the family (E _i ) _iI of spaces is

On Relations Between Bessel Potential Spaces and Riesz Potential Spaces

We present a relation between the Bessel potential spaces and the Riesz potential spaces. The ideas of the proof are to characterize each potential spaces and to give a correspondence between individual Bessel potentials and Riesz potentials.     

矢值序列空间上的一类无穷矩阵变换

对于一类经典的矢值序列空间,文中引入了一类重要子集,它包括了该序列空间的全部全有界集和许多非全有界集．利用Antosik-Mikusinski基本矩阵定理和该子集族,对于一类映射矩阵获得了一个无穷矩阵收敛定理,并且给出了一类经典无穷矩阵变换的更强刻划．此结果补充和完善了非线性矩阵变换定理．     

Measure of Noncompactness of Linear Operators between Spaces of Sequences That Are (N,q) Summable or Bounded

In this paper we investigate linear operators between arbitrary BK spaces X and spaces Y of sequences that are summable or bounded. We give necessary and sufficient conditions for infinite matrices A to map X into Y. Further, the Hausdorff measure of noncompactness is applied to give necessary and sufficient conditions for A to be a compact operator.     

紧支撑多重向量值正交小波包的性质

给出紧支撑多重向量值正交小波包的定义及构造方法.运用矩阵理论与积分变换,研究了多重向量值正交小波包的性质,得到三个正交性公式.进而,得到空间L2(R,Cr)的一个新的规范正交基.