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1.
Gliding hump properties of matrix domains   总被引:2,自引:0,他引:2  
Gliding hump properties play an important role in numerous topics in analysis, for instance, they are used as a substitute for the uniform boundedness principle. Since examples of sequence spaces having certain gliding hump properties are rare, the main aim of this paper is to present classes of infinite matrices A such that the matrix domain E A has a certain gliding hump property whenever a given sequence space E has this property.  相似文献   

2.
Let λ and μ be sequence spaces and have both the signed-weak gliding hump property, (λ,μ) the algebra of the infinite matrix operators which transform λ into μ. In this paper, it is proved that if λ and μ are β-spaces and λ^β and ,μ^β have also the signed-weak gliding hump property, then for any polar topology τ, ((λ,μ),τ) is always sequentially complete locally convex topological algebra.  相似文献   

3.
Letωbethespaceofallscalarvaluedsequences,and φitssubspacewithonlyfinitelymanynon zerocoordinates.AlinearsubspaceEofωiscalledasequencespace. Wesaythatanon zerovectorsequence {z(n) }inωisablocksequenceifthereexistsastrictlyincreasingsequenceofpositiveinteger…  相似文献   

4.
We are studying complete and B-complete topological vector groups. These Objects have been introduced by P. Kenderov [6] and D. A. Raikov [11]. They form a category TVG intermediate to the categories of topological Abelian groups and topological vector spaces and are close enough to the last one to give many useful applications to it. We first consider the problem of completion in the most used subcategories of TVG. A special functor allows to play back permanence property questions of completeness in locally convex vector groups to the same questions for locally convex vector spaces. Some examples of complete locally convex vector groups follow. We then unify some differently defined notions of B-completeness and generalize well known theorems concerning B-complete locally convex topological vector spaces to locally convex topological vector groups. Barrelledness concepts introduced in 9 and a special functor constructed in section 6 are used to formulate analogues of the closed graph and open mapping theorem for locally convex vector groups. The remainder of the note is left for applications to locally convex vector spaces. Many theorems about 1p-sums of normed spaces are proved, as well as the B-completeness of a vast class of locally convex vector spaces including the spaces and of Köthe ([7], §13, No 5,6).  相似文献   

5.
《Mathematische Nachrichten》2018,291(4):610-631
We research proximinality of μ‐sequentially compact sets and μ‐compact sets in measurable function spaces. Next we show a correspondence between the Kadec–Klee property for convergence in measure and μ‐compactness of the sets in Banach function spaces. Also the property S is investigated in Fréchet spaces and employed to provide the Kadec–Klee property for local convergence in measure. We discuss complete criteria for continuity of metric projection in Fréchet spaces with respect to the Hausdorff distance. Finally, we present the necessary and sufficient condition for continuous metric selection onto a one‐dimensional subspace in sequence Lorentz spaces .  相似文献   

6.
In this paper, we obtain new results for the weak‐AFPP in abstract spaces by exploiting biorthogonal systems techniques. Firstly, we investigate the strong‐AFPP on countably infinite dimensional Hausdorff locally convex spaces. Spaces of this class are shown to be sequentially complete iff they have the hereditary FPP for totally bounded, closed convex sets. This might open a research line for the analysis of weak‐AFPP in such frames. In connection, we provide a simple criterion for the containement of ?1‐sequences in terms of strongly‐equicontinuous biorthogonal systems. We then establish a few results concerning the existence of Hausdorff finer vector topologies on abstract spaces having as prescribed condition the existence of such systems. The proofs are based on methods of Peck and Porta concerning building of finer vector topologies, and a classical construction of Singer which allows us to prove under rather natural conditions the existence of equicontinuous biorthogonal systems in metrizable locally convex spaces. These results are compatible with the failure of the weak‐AFPP. We also study the inverse problem by proving that every infinite dimensional vector space admits a (non‐locally convex) Hausdorff vector topology which is complete, non‐metrizable and is compatible with a bounded Hamel Schauder basis. It is shown further that such a topology has the ‐AFPP, where is the linear span of coefficient functionals associated to a Hamel basis. Finally, inspired by a result of Shapiro, we observe that if X is a non‐locally convex F‐space with an absolute basis, then the weak‐AFPP is equivalent to the fact that every bounded convex subset of X is compact.  相似文献   

7.
In this note, we establish several results concerning the gliding hump properties of matrix domains. In order to discuss F-WGHP, we introduce the UAK-property and find that this sort of property has close relationship with F-WGHP. In the course of discussing F-WGHP and WGHP of (C0)cn, we discuss the F-WGHP and WGHP of the almost-null sequence space f0.  相似文献   

8.
This article is concerned with ultradistribution spaces in the sense of Komatsu. For these spaces several tensor product theorems, especially Schwartz's kernels theorem for ultradistributions, are proved. Criteria which ensure that a nuclear locally convex space has an absolute basis are given and used to represent the spaces of periodic ultradifferential functions as Köthe sequence spaces. These results permit to state conditions on a sequence {Mp} which are equivalent to nuclearity, s-nuclearity or-as will be shown in part II-even -nuclearity of the corresponding ultradistribution spaces. Under some natural conditions the Beurling ultradistribution spaces defined by Komatsu are shown to constitute a proper subclass of those introduced by Beurling.  相似文献   

9.
10.
给出F-弱滑脊性的定义,利用此性质,证明如果λ是一个具有F-弱滑脊性的数量空间,λ-乘数无序收敛是一个对偶不变性.如果(λ,β(λ,λ~(uβ)))是FAK-空间,则上述性质变成全程不变性.  相似文献   

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