弱Orlicz鞅空间的弱原子分解及其应用

对3类由凹函数生成的弱Orlicz鞅空间建立了相应的弱原子分解.作为应用,首先给出了这些弱Orlicz鞅空间上次线性算子有界的一个充分条件,并在此基础上证明了一些弱型鞅不等式,然后证明了关于这些弱Orlicz鞅空间的Marcinkiewicz型插值定理.     

关于线性算子的右有界拟线性内逆

对于从线性空间到赋范线性空间的线性算子T引入右有界拟线性内逆的概念.在算子值域的闭包R(T)为切比雪夫子空间的条件下,给出右度量内逆的表示.证得:如果算子的值域R(T)非闭且闭包R(T)为切比雪夫的,则必存在不同的右有界拟线性内逆.     

具有线性扰动的线性脉冲微分系统的有界增长

本文介绍了脉冲微分系统的有界增长的概念，并进一步讨论了具有线性扰动的线性脉冲微分系统的有界增长问题，得到了反映无扰和扰动两种情形下脉冲微分系统有界增长关系的定理。     

无限时滞线性中立型泛函微分方程周期解 (英)

本文以Cg空间为相空间,证明了具无限时滞D算子型线性中立型泛函微分方程存在周期解当且仅当存在有界解,得到了与以往结论互不包含的结果．     

半序线性空间上线性泛函的两个Gr\"{u}ss型不等式$^{}$

证明了半序线性空间上线性泛函的两个Gr\"{u}ss型不等式, 并由此给出了Karamata型积分不等式的一种推广形式, 得到了一个新的Gr\"{u}ss型积分不等式及关于傅立叶系数的两个不等式. 最后利用所得结论研究了关于矩阵及线性算子的一些Gr\"{u}ss型不等式.     

$I$-模糊拓扑空间中的模糊紧度

本文借助不等式给出了$I$-模糊拓扑空间中模糊紧度的概念, 并研究了相关的性质.     

一类不可分解Banach空间上线性算子的谱性质

给出一类不可分解的∑_e~1型Banach空间上线性算子(不一定有界)的谱结构,并讨论这种空间上生成C_0群或C_0半群的线性算子的有界性、特殊的谱性质和谱结构,还给出这种空间上闭算子是有界算子的一个充分条件。     

Ｐ型基和良性有界算子

在自反Ｂａｎａｃｈ空间上一个有界线性算子是（Ｂ）型良性有界的当且仅当它的共扼算子也是（Ｂ）型的。但在非自反Ｂａｎａｃｈ空间上这种性质不成立。本文证明在一大类非自反Ｂａｎａｃｈ空间上总存在一个（Ｂ）型良性有界线性算子，它的共扼算子不是（Ｂ）型的。同时也证明了在具有基的Ｂａｎａｃｈ空间上，任何Ｐ型基序列一定有一个子序弄能够扩张成该空间的一个基。     

一类带有组合非线性项Kirchhoff方程解的多重性

本文研究一类全空间上的Kirchhoff型方程.当非线性项在无穷远处是线性有界时,利用变分方法建立方程解的多解性结果,并讨论次线性项对问题解的多重性的具体影响,改进了相关文献中的结论.     

桶型空间的一些注记

Husain和Wong引进了s桶空间概念,统一处理桶空间和拟桶空间.本文给出各种S桶空间的特征,一个Banach-steinhaus型的结果以及一个S桶空间与S吸囿空间的关系的定理. 文中(E,(?)),(F,φ)是T_2局部凸拓扑线性空间.E＇是E的拓扑对偶空间.由E的某些(?)有界集组成的集族S称为E＇的拓扑化族是指s满足E={B∶B∈S}.L(E,F)上的在s上一致收敛的拓扑记为(?)_s(F).当F为数域K时.(?)_s(K)记为(?)_s.(?)_s便是E＇上的在S上一致收敛的拓扑.E＇上的全部(?)_s有界集(?)是一个E的拓扑化族.E上的在(?)上一致收敛的拓扑     

The Construction of I-Bornological Vector Spaces

In this paper, the concept of I-bornological vector spaces and two examples of the spaces are given. Two methods on constructing new I-bornological vector spaces are discussed,one is using a(crisp) bornological vector space to induce an I-bornological vector space, the other is utilizing I-bornological linear maps to generate an I-bornological vector space.     

On -topological vector spaces generated by a co-tower of L-topological vector spaces

In this paper, a characterization for an I(L)-topological space to be generated by a given co-tower of L-topological spaces is obtained. Moreover, the relationship between some properties of an I(L)-topological vector space generated by a co-tower of L-topological vector spaces and the corresponding properties of the given co-tower of L-topological vector spaces is investigated. Our results show that if an I(L)-topological vector space generated by a co-tower of L-topological vector spaces has some properties, such as local convexity and local boundedness, then all L-topological vector spaces in the co-tower also have the same properties. But the converse is incorrect even in the case of I-topological vector space generated by a co-tower of classical topological vector spaces. Finally, we supply a necessary and sufficient condition for an I(L)-topological vector space generated by a co-tower of L-topological vector spaces with some properties, such as local convexity and local boundedness, to have such properties too.     

On quasilinear spaces of convex bodies and intervals

Algebraic systems abstracting properties of convex bodies and intervals, with respect to addition and multiplication by scalars, known as quasilinear spaces, are studied axiomatically. We discuss special quasilinear spaces with group structure called quasivector spaces. We show that every quasivector space is a direct sum of a vector space and a symmetric quasivector space. A complete characterization of symmetric quasivector spaces in the finite dimensional case is given, which permits to reduce computation in quasilinear spaces to computation in familiar vector spaces.     

Abstract capacitary estimates and the completeness and separability of certain classes of non-locally convex topological vector spaces

We are concerned with establishing completeness and separability criteria for large classes of topological vector spaces which are typically non-locally convex, including Lebesgue-like spaces, Lorentz spaces, Orlicz spaces, mixed-normed spaces, tent spaces, and discrete Triebel–Lizorkin and Besov spaces. For vector spaces of measurable functions we also derive pointwise convergence results. Our approach relies on abstract capacitary estimates and works in certain cases of interest even in the absence of a background measure space and/or of a vector space structure.     

A characterisation of inner product spaces by the maximal circumradius of spheres

We give a new characterisation of inner product spaces amongst normed vector spaces in terms of the maximal circumradius of spheres. It turns out that a normed vector space is an inner product space if and only if all spheres are not degenerate, i.e., the maximal circumradius of points on the sphere equals the radius of the sphere.     

On an equivalence of topological vector space valued cone metric spaces and metric spaces

Scalarization method is an important tool in the study of vector optimization as corresponding solutions of vector optimization problems can be found by solving scalar optimization problems. Recently this has been applied by Du (2010) [14] to investigate the equivalence of vectorial versions of fixed point theorems of contractive mappings in generalized cone metric spaces and scalar versions of fixed point theorems in general metric spaces in usual sense. In this paper, we find out that the topology induced by topological vector space valued cone metric coincides with the topology induced by the metric obtained via a nonlinear scalarization function, i.e any topological vector space valued cone metric space is metrizable, prove a completion theorem, and also obtain some more results in topological vector space valued cone normed spaces.     

Frames for vector spaces and affine spaces

A finite frame for a finite dimensional Hilbert space is simply a spanning sequence. We show that the linear functionals given by the dual frame vectors do not depend on the inner product, and thus it is possible to extend the frame expansion (and other elements of frame theory) to any finite spanning sequence for a vector space. The corresponding coordinate functionals generalise the dual basis (the case when the vectors are linearly independent), and are characterised by the fact that the associated Gramian matrix is an orthogonal projection. Existing generalisations of the frame expansion to Banach spaces involve an analogue of the frame bounds and frame operator.The potential applications of our results are considerable. Whenever there is a natural spanning set for a vector space, computations can be done directly with it, in an efficient and stable way. We illustrate this with a diverse range of examples, including multivariate spline spaces, generalised barycentric coordinates, and vector spaces over the rationals, such as the cyclotomic fields.     

Ideals and bands in pre-Riesz spaces

In a vector lattice, ideals and bands are well-investigated subjects. We study similar notions in a pre-Riesz space. The pre-Riesz spaces are exactly the order dense linear subspaces of vector lattices. Restriction and extension properties of ideals, solvex ideals and bands are investigated. Since every Archimedean directed partially ordered vector space is pre-Riesz, we establish properties of ideals and bands in such spaces.      

ON VECTOR SPACES WITH LOCALLY BOUNDED CONVERGENCE STRUCTURES

ABSTRACT

It is known that a precompact set in a limit vector space is not necessarily bounded. In this paper it is shown that the topological vector space result that every precompact set is bounded can be extended to the large class of locally bounded prelimit vector spaces. This result is used to extend the well-known characterization of finite-dimensional separated topological vector spaces to locally bounded prelimit vector spaces.     

Lokalkreisförmige Vektorgruppen

We define locally circled vector groups as topological vector spaces over the discrete real or complex numberfield with a neighbourhoodbase of zero consisting of circled sets. Every topological vector space is a locally circled vector group. Topological vector groups and especially locally circled vector groups have useful applications to topological vector spaces and this paper is intended as an introduction to the theory of locally circled vector groups. Continuations including applications to topological vector spaces will follow. Here we study the structure of finite dimensional and locally compact vector groups, describe those locally circled vector groups which have a generating precompact circled set and finally prove some theorems about convex sets in these spaces.