Remotality of Closed Bounded Convex Sets in Reflexive Spaces

Let X be a Banach space and E be a closed bounded subset of X. For x ? X, we define D(x, E) = sup{‖ x ? e‖:e ? E}. The set E is said to be remotal (in X) if, for every x ? X, there exists e ? E such that D(x, E) = ‖x ? e‖. The object of this paper is to characterize those reflexive Banach spaces in which every closed bounded convex set is remotal. Such a result enabled us to produce a convex closed and bounded set in a uniformly convex Banach space that is not remotal. Further, we characterize Banach spaces in which every bounded closed set is remotal.     

弱紧集与Orlicz空间

本文圆满完善了[1]的结果,并由此给出了Ｏｒｌｉｃｚ空间自反性与Ｓｈｕｒ定理的新证明。     

On the Duality Mapping Sets in Orlicz Sequence Spaces

The criteria for the weak compactness of duality mapping sets J(x) = {f∈X* : <f, x> = ∥f∥² = ∥x∥²} in Orlicz sequence spaces endowed either with the Luxemburg norm or with the Orlicz norm are obtained. Supported by the National Natural Science Foundation of China, Grants 19901007 and 19871020     

Orlicz序列空间的对偶映射

本文研究Orlicz序列空间的对偶映射,给出对偶映象集为弱紧集的充分必要 条件.作为推论,得到Orlicz序列空间的弱接近光滑性的充要条件.     

Banach空间上凸集的凸性

以Banach空间的一般凸集为研究对象,将Banach空间的凸性研究推广到了内部非空的凸集上．打破了从单位球出发研究Banach空间几何的具有局限性的研究方法,给出了严格凸集的若干特征刻画及性质,并得到了严格凸集和光滑集之间的对偶定理．     

Slice-Continuous Sets in Reflexive Banach Spaces: Some Complements

In this paper we study a class of closed convex sets introduced recently by Ernst et al. (J Funct Anal 223:179–203, 2005) and called by these authors slice-continuous sets. This class, which plays an important role in the strong separation of convex sets, coincides in ℝ ⁿ with the well known class of continuous sets defined by Gale and Klee in the 1960s. In this article we achieve, in the setting of reflexive Banach spaces, two new characterizations of slice-continuous sets, similar to those provided for continuous sets in ℝ ⁿ by Gale and Klee. Thus, we prove that a slice-continuous set is precisely a closed and convex set which does not possess neither boundary rays, nor flat asymptotes of any dimension. Moreover, a slice-continuous set may also be characterized as being a closed and convex set of non-void interior for which the support function is continuous except at the origin. Dedicated to Boris Mordukhovich in honour of his 60th birthday.     

一种新的集合序列收敛性

本我们引进了无穷维Ｂａｎａｃｈ空间中的一种新的集合序列收敛性概念,讨论了它与其它收敛性概念的关系。另外,我们还研究了集合序列根限的Ｍｉｎｋｏｗｓｋｉ和。     

Orlicz空间的小波

利用小波系数给出Orlicz空间的一个特征,并研究小波展开的无条件收敛性.     

Connectedness of Cone Superefficient Point Sets in Locally Convex Topological Vector Spaces

This paper studies the connectedness of the cone superefficient point set in locally convex topological vector spaces. First, we prove a scalarization theorem for a cone superefficient point set. From this result, we obtain the connectedness of a cone superefficient point set under the conditions that the set is cone convex and cone weakly compact.     

Orlicz空间的一组不等式

本文将LL~p空间的特征不等式部分地推广到了赋Orlicz范数的Orlicz空间L_M~*中,运用Orlicz空间理论的方法,获得了Orlicz空间L_M~*的一组不等式.     

Minimal Blocking Sets in Projective Spaces of Square Order

In this paper minimal m-blocking sets of cardinality at most in projective spaces PG(n,q) of square order q, q 16, are characterized to be (t, 2(m-t-1))-cones for some t with . In particular we will find the smallest m-blocking sets that generate the whole space PG(n,q) for 2m n m.     

Parabolic Equations in Orlicz Spaces

An approximation theorem in inhomogeneous Orlicz–Sobolevspaces is proved which allows a second-order parabolic equationin Orlicz spaces to be solved. A trace result is also givenwhich shows that the solutions are continuous with respect totime.     

Orlicz空间的P凸性

赋Orlicz范数的Orlicz空间的P凸等价于自反。     

Lacunary Sets and Function Spaces with Finite Cotype

We investigate translation invariant subspaces of the space of uniformly convergent Fourier series and Orlicz spaces, with finite cotype. In the case of Orlicz spaces, this leads to some new characterizations of p-Rider sets.     

Amemiya Norm Equals Orlicz Norm in Musielak-Orlicz Spaces

Let （Ω,μ） be a a-finite measure space and Φ ： Ω × [0,∞） → [0, ∞] be a Musielak-Orlicz function. Denote by L^Φ（Ω） the Musielak-Orlicz space generated by Φ. We prove that the Amemiya norm equals the Orlicz norm in L^Φ（Ω）.     

Compact Embeddings of Besov Spaces in Exponential Orlicz Spaces

Let 1 < p < , 0 < v < p', let be a bounded domainin Rⁿ, and denote by id the limiting compact embedding of theBesov space (Rⁿ) into the exponentialOrlicz space L_exp(t^v)(), mapping a function f onto its restrictionf|. In 1993 Triebel established, among others, two-sided estimatesfor the entropy numbers of id, which are even asymptoticallyoptimal for ‘small’ . The aim of the paper is toimprove the upper bounds in the case of ‘large’, where Triebel's estimates are not yet sharp, thus making afurther step towards the conjectured correct asymptotic behaviour.     

On Decomposition in Exponential Orlicz Spaces

Various characterizations are given of the exponential Orlicz space L and the Orlicz‐Lorentz space L. By way of application we give a simple proof of the celebrated theorem of Brézis and Wainger concerning a limiting case of a Sobolev imbedding theorem.     

Instability of Capacity in Orlicz Spaces

In this paper we describe the instability of certain capacities in the Orlicz spaces. Our results generalize some of those obtained by Fernström in [6] and the Theorem 9 of Hedberg in [7] in the case of Lebesgue spaces.     

WCS Coefficients in Orlicz Sequence Spaces

We introduce some practical calculation of the weakly convergent sequence coefficients of Orlicz sequence spaces equipped with Luxemburg norm and Orlicz norm. For the N-function (u) of which the index function is monotonuous, the exact value WCS(l⁽⁾) of Orlicz sequence space l⁽⁾ with Luxemburg norm is available, i.e. WCS(l⁽⁾) = or WCS(l) of l with Orlicz norm has the exact value or estimation

Best Local Approximation in Orlicz Spaces

We get results in Orlicz spaces L ^φ about best local approximation on non-balanced neighborhoods when φ satisfies a certain asymptotic condition. This fact generalizes known previous results in L ^p spaces.