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1.
In this article, using generalized weighted mean and difference matrix of order m, we introduce the paranormed sequence space ?(u, v, p; Δ(m)), which consist of the sequences whose generalized weighted Δ(m)-difference means are in the linear space ?(p) defined by I.J. Maddox. Also, we determine the basis of this space and compute its α-, β- and γ-duals. Further, we give the characterization of the classes of matrix mappings from ?(u, v, p, Δ(m)) to ?, c and c0. Finally, we apply the Hausdorff measure of noncompacness to characterize some classes of compact operators given by matrices on the space ?p(u, v, Δ(m))(1 ≤ p < ∞).  相似文献   

2.
Orlicz序列空间的弱收敛序列系数   总被引:3,自引:0,他引:3  
本文给出了Orlicz序列空间的弱收敛序列系数的表达式.  相似文献   

3.
This paper deals with function spaces of varying smoothness. It is a modified version of corresponding parts of [8]. Corresponding spaces of positive smoothness s (x) will be considered in part II. We define the spaces Bp (?n ), where the function ??: x ? s (x) is negative and determines the smoothness pointwise. First we prove basic properties and then we use different wavelet decompositions to get information about the local smoothness behavior. The main results are characterizations of the spaces Bp (?n ) by weighted sequence space norms of the wavelet coefficients. These assertions are used to prove an interesting connection to the so‐called two‐microlocal spaces Cs,s (x0). (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)  相似文献   

4.
本文证明如果奥尔里奇函数M满Δ2条件并且liminfb→0limsupa→0M(ab)/M(a)M(b)=0或者limsupb→0liminfa→0M(ab)/M(a)M(b)=0那么奥尔里序列空间lM不同构于它的由标准基的块基(其系数趋向于零)张成的任何子空间  相似文献   

5.
6.
Given three Banach spaces X, Y and Z and a bounded bilinear map , a sequence x=n(xn)⊆X is called B-absolutely summable if is finite for any yY. Connections of this space with are presented. A sequence x=n(xn)⊆X is called B-unconditionally summable if is finite for any yY and zZ and for any MN there exists xMX for which nMB(xn,y),z〉=〈B(xM,y),z〉 for all yY and zZ. A bilinear version of Orlicz-Pettis theorem is given in this setting and some applications are presented.  相似文献   

7.
《Quaestiones Mathematicae》2013,36(4):299-313
ABSTRACT

Let Λ be a scalar sequence space which is endowed with a normal locally convex topology. For a separated locally convex space E we denote by Λ(E) the vector space of all sequences g in E for which (>g(i),a<) ε Λ for all a ε E'. We define a locally convex topology ζ on Λ(E) and then characterize the dual of the ζ-closure (denoted by Λc (E)) of the finite sequences in Λ(E). We demonstrate the existence of a continuous projection from Λ(E)' onto a subspace of Λ(E)' which is isomorphic to Λc(E)'. Furthermore, we find a topological decomposition of Λα c (E)”, where one of the factors is isomorphic to Λ;α(E). These results are then applied to find necessary and sufficient conditions for Λα(E) to be semi-reflexive. A parallel development yields the same results for the space Λ(E') of all sequences f in E' for which (>x, f(i)<) ε Λ; for all x ε E, when E is barrelled. We conclude the paper by application of the results on vector sequence spaces to spaces of operators—including for instance, necessary and sufficient conditions for Lb (E,Λ;) and Lb (Λ,E) to be semi-reflexive.  相似文献   

8.
In this paper, we have discussed the weakly convergent sequence coefficient in Köthe sequence spaces with as their boundedly complete basis. Using those results, we can easily calculate the weakly convergent sequence coefficient in Orlicz sequence spaces.

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9.
本文证明了Schur空间与有限维Banach空间的两个特征定理,并对赋范线性空间中的列收敛进行了讨论,得到了一些有趣的结果。  相似文献   

10.
In this paper, the sequence spaces e0^τ(u, p) and ec^τ(u, p) of non-absolute type which are the generalization of the Maddox sequence spaces have been introduced and it is proved that the spaces e0^τ(u,p) and ec^τ(u,p) are linearly isomorphic to spaces co(p) and c(p), respectively. Furthermore, the α-, β- and γ-duals of the spaces 0^τ(u,p) and ec^τ(u,p) have been computed and their bases have been constructed and some topological properties of these spaces have been investigated. Besides this, the class of matrices (e0^τ)(u, p) : μ) has been characterized, where μ is one of the sequence spaces l∞, c and co and derives the other characterizations for the special cases of μ. In the last section, Euler Core of a complex-valued sequence has been introduced, and we prove some inclusion theorems related to this new type of core.  相似文献   

11.
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 Fr(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.  相似文献   

12.
13.
本文给出赋Orlicz范数和赋Luxemburg范数的Orlicz序列空间的单位球面上的强暴露点的充分必要条件.  相似文献   

14.
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 Fr(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.  相似文献   

15.
16.
LetL(X, Y) be the Banach space of all continuous linear operators fromX toY, and letK(X, Y) be the subspace of compact operators. Some versions of the classical Pitt theorem (ifp>q, thenK(l p, lq)=L(lp, lq)) for subspaces of Lorentz and Orlicz sequence spaces are established. Translated fromMatematicheskie Zametki, Vol. 61, No. 1, pp. 18–25, January, 1997. Translated by V. N. Dubrovsky  相似文献   

17.
Let L be a Schr?dinger operator of the form L =-Δ + V acting on L~2(R~n) where the nonnegative potential V belongs to the reverse H?lder class B_q for some q ≥ n. In this article we will show that a function f ∈ L~(2,λ)(R~n), 0 λ n, is the trace of the solution of L_u =-u_(tt) + L_u =0, u(x, 0) = f(x), where u satisfies a Carleson type condition sup x_B,r_Br_B~(-λ)∫_0~(rB)∫_(B(x_B,r_B))t|u(x,t)|~2dxdt≤C∞.Its proof heavily relies on investigate the intrinsic relationship between the classical Morrey spaces and the new Campanato spaces L_L~(2,λ)(R~n) associated to the operator L, i.e.L_L~(2,λ)(R~n)=L~(2,λ)(R~n).Conversely, this Carleson type condition characterizes all the L-harmonic functions whose traces belong to the space L~(2,λ)(R~n) for all 0 λ n.  相似文献   

18.
薛学梅 《数学研究》2009,42(2):138-153
本文主要讨论抽象度量空间上的一致连续函数空间的Banach空间结构,代数结构和格结构.  相似文献   

19.
We investigate the problem of the uniqueness of the extension of -homogeneous polynomials in Banach spaces. We show in particular that in a nonreflexive Banach space that admits contractive projection of finite rank of at least dimension 2, for every there exists an -homogeneous polynomial on that has infinitely many extensions to . We also prove that under some geometric conditions imposed on the norm of a complex Banach lattice , for instance when satisfies an upper -estimate with constant one for some , any -homogeneous polynomial on attaining its norm at with a finite rank band projection , has a unique extension to its bidual . We apply these results in a class of Orlicz sequence spaces.

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20.
Bessel sequence plays an important role in the study of frames for a Hilbert space with the convergence of a frame series, which has been widely studied in the literature. This paper addresses multi-wavelet Bessel sequences in Sobolev spaces setting, the result obtained is useful for the study of multi-wavelet frames in these spaces.  相似文献   

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