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].     

Nonabsolute Integral on Measure Spaces

We define a Henstock-type integral on measure spaces with metrictopologies, and give an example of a function which is integrablebut whose absolute value is not. 1991 Mathematics Subject Classification26A39, 46G12.     

On Some Expressions for the Riesz Angles of Orlicz Sequence Spaces

We obtain some expressions for the Riesz angles of Orlicz sequence spaces endowed with the Luxemburg and Orlicz norms and show some practical ways of computation.     

On Complemented Subspaces of Some Koethe Spaces of Infinite Type

There is a basis for each complemented subspace of a Koethe space in the Dragilev class of type 1.     

Matrix Transformations Between Some Vector-Valued Sequence Spaces

In this paper, we give necessary and sufficient conditions for infinite matrices mapping from the Nakano vector-valued sequence space (X, p) into any BK-space, and by using this result, we obtain the matrix characterizations from (X, p) into the sequence spaces (Y), c₀(Y, q), c(Y), _s(Y), E_r(Y), and F_r(Y), where p = (p_k) and q = (q_k) are bounded sequences of positive real numbers such that p_k 1 for all k N, r 0, and s 1.AMS Subject Classification (2000): 46A45     

On Euler Equations in Higher Order Sobolev Spaces

We consider the integral functional of calculus of variations involving higher order derivatives. It is shown that any local minimum of the functional solves the associated strongly nonlinear elliptic problem in a certain weak sense in spite of the fact that no growth conditions are imposed on the zero order term.     

Musielak-Orlicz序列空间中的S-点

本文给出了Musielak-Orlicz序列空间中S-点的充要判别准则.作为推论,得到Musielak-Orlicz序列空间具有S-性质的充分必要条件.     

On Some Local Geometry of Orlicz Sequence Spaces Equipped with the Luxemburg Norm

Criteria for strong U-points, compactly locally uniformly rotund points, weakly compactly locally uniformly rotund points and locally uniformly rotund-points in Orlicz sequence spaces equipped with the Luxemburg norm are given. It is also shown that in any Banach space X strong U-points are exposed points and that these points are related to very smooth points in the dual space X*.     

关于一类姜空间

在这篇注记中,利用群的作用我们提供了一类姜空间。     

On Some Applications of Geometry of Banach Spaces and Some New Results Related to the Fixed Point Theory in Orlicz Sequence Spaces

We present some applications of the geometry of Banach spaces in the approximation theory and in the theory of generalized inverses. We also give some new results, on Orlicz sequence spaces, related to the fixed point theory. After a short introduction, in Section 2 we consider the best approximation projection from a Banach space $X$ onto its non-empty subset and proximinality of the subspaces of order continuous elements in various classes of Köthe spaces. We present formulas for the distance to these subspaces of the elements from the outside of them. In Section 3 we recall some results and definitions concerning generalized inverses of operators (metric generalized inverses and Moore-Penrose generalized inverses). We also recall some results on the perturbation analysis of generalized inverses in Banach spaces. The last part of this section concerns generalized inverses of multivalued linear operators (their definitions and representations). The last section starts with a formula for modulus of nearly uniform smoothness of Orlicz sequence spaces $\ell^\Phi$equipped with the Amemiya-Orlicz norm. From this result a criterion for nearly uniform smoothness of these spaces is deduced. A formula for the Domínguez-Benavides coefficient $R(a,l_\Phi)$ is also presented, whence a sufficient condition for the weak fixed point property of the space $\ell^\Phi$is obtained.     

On Some Special Pseudoconvex Spaces

We present two ways of constructing pseudoconvex spaces. The first theorem states that an interval space is pseudoconvex if the intervals are range sets of continuous functions and a cone erected to a convex set is convex. Secondly, if H is pseudoconvex and in the Cartesian product H × Rthe intervals are defined by going first along the H-segment, then along the R-segment (the other coordinates fixed) then H × Ris pseudoconvex.     

Some of Commutators on Spaces of Homogeneous Type

§ 1.Ｉｎｔｒｏｄｕｃｔｉｏｎ　Ｌｅｔａｂｅａｍｅａｓｕｒａｂｌｅｆｕｎｃｔｉｏｎ ,ｂｅａ φ∈Ｓ(Ｒ)ｎｏｎｎｅｇａｔｉｖｅｆｕｎｃｔｉｏｎ ,ａｎｄ 0 <ｒ <∞ .Ｄｅｆｉｎｅｃｏｍｍｕｔａｔｏｒｓａｓｆｏｌｌｏｗｓ :Ｃｒａ( ｆ) (ｘ) =ｓｕｐｘ∈Ｑ1｜Ｑ｜∫Ｑ｜ａ(ｘ) -ａ( ｙ) ｜ｒ｜ｆ( ｙ) ｜ｄｙ ,( 1 .1 )ａｎｄΦｒａ( ｆ) (ｘ) =ｓｕｐε>0∫Ｒｎ｜ａ(ｘ) -ａ( ｙ) ｜ｒφε( ｜ｘ- ｙ｜)｜ｆ( ｙ) ｜ｄｙ ,( 1 .2 )ｗｈｅｒｅＱｄｅｎｏｔｅｓａｃｕｂｅａｎｄφε(ｔ) =1εｎφ ｔε .Ｔｈｅｓｅｔｗｏｏｐｅｒａｔ…     

Some Results Related to Metric Projection in Orlicz Sequence Spaces

Let X be a Banach space,and D a subset of X.A metric projection PD:X→ 2 Dis de-fined by PD(x) ={ y∈ D:‖ x-y‖ =d(x,D) } .D is a proximal (resp.Chebysev) setif PD contains at least(resp.exactly) one point.For a proximal set D,PD is callednorm-norm(norm-week) upper semi-continuous at x if for every normed(weak) openset W PD,there exists a normed neighborhood U of x such that PD(y) W for all y inU.It is proved in[1 ] that if X has C- (C- ) property PDis continuous for a Cheby-sev…     

On a Beurling-Arveson Type Theorem for Some Functional Hilbert Spaces and Related Questions

We prove in terms of Berezin symbols a Beurling-Arveson type theorem for some functional Hilbert space over the unit disc of the complex plane . We give also an affirmative answer to a question of Yang [15].      

关于某些广义可数紧空间

We first give alternative expressions of some generalized countably compact spaces such as quasi-γ spaces, quasi-Nagata spaces, M#-spaces and wM-spaces with g-functions. Then by means of these expressions, we present some characterizations of the corresponding spaces with real-valued functions.     

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.     

关于某些拟一致空间的超空间拓扑

设(X,τ)是一个拓扑空间。在本文中,我们证明了在超空间2^X上局部有限拓扑e^τ与局部有限覆盖拟一致u_LF所导出的超拓扑|2^u_LF|是相同的。我们还证明了下面条件是等价的:(1)(X,τ)是仿紧的;(2)(X,τ)是orth紧的,且e^τ=|2^u_FT|;(3)存在一个Lebes-yue拟一致u_L,使e^τ<