首页 | 本学科首页   官方微博 | 高级检索  
相似文献
 共查询到20条相似文献,搜索用时 109 毫秒
1.
In this paper, we give some characterizations of metric spaces under weak-open π-mappings, which prove that a space is g-developable (or Cauchy) if and only if it is a weak-open π-image of a metric space.  相似文献   

2.
The main results of this paper are that (1) a space X is g-developable if and only if it is a weak-open π image of a metric space, one consequence of the result being the correction of an error in the paper of Z. Li and S. Lin (2) characterizations of weak-open compact images of metric spaces, which is another answer to a question in in the paper of Y. Ikeda, C. liu and Y. Tanaka.  相似文献   

3.
In this paper, we show, among other results, that if X is a [separable] locally compact space X [satisfying the first countability axiom] then the space Cc (X) has countable tightness [if and only if it has bounding tightness] if and only if it is Frechet-Urysohn, if and only if Cc (X) contains a dense (LM) subspace and if and only if X is a-compact.  相似文献   

4.
Let X denote a specific space of the class of X α,p Banach sequence spaces which were constructed by Hagler and the first named author as classes of hereditarily ℓp Banach spaces. We show that for p > 1 the Banach space X contains asymptotically isometric copies of ℓp. It is known that any member of the class is a dual space. We show that the predual of X contains isometric copies of ℓp where 1/p + 1/q = 1. For p = 1 it is known that the predual of the Banach space X contains asymptotically isometric copies of c 0. Here we give a direct proof of the known result that X contains asymptotically isometric copies of ℓ1.  相似文献   

5.
We give sufficient conditions on Banach spaces X and Y so that their projective tensor product Xπ Y, their injective tensor product Xɛ Y, or the dual (Xπ Y)* contain complemented copies of ℓp.  相似文献   

6.
We show that every contractive C 0-semigroup on a separable, infinite-dimensional Hilbert space X can be approximated by unitary C 0-groups in the weak operator topology uniformly on compact subsets of ℝ+. As a consequence we get a new characterization of a bounded H -calculus for the negatives of generators of bounded holomorphic semigroups. Applications of our results to the study of a topological structure of the set of (almost) weakly stable contractive C 0-semigroups on X are also discussed. The author was partially supported by the Marie Curie “Transfer of Knowledge” programme, project “TODEQ”, and by a MNiSzW grant Nr. N201384834.  相似文献   

7.
An elementary proof of the (known) fact that each element of the Banach space w p (X) of weakly absolutelyp-summable sequences (if 1≤p<∞) in the Banach spaceX is the norm limit of its sections if and only if each element of w p (X) is a norm null sequence inX, is given. Little modification to this proof leads to a similar result for a family of Orlicz sequence spaces. Some applications to spaces of compact operators on Banach sequence spaces are considered.  相似文献   

8.
Let π be a set of primes and G a π-separable group. Isaacs defines the B π characters, which can be viewed as the “π-modular” characters in G, such that the B p′ characters form a set of canonical lifts for the p-modular characters. By using Isaacs’ work, Slattery has developed some Brauer’s ideals of p-blocks to the π-blocks of a finite π-separable group, generalizing Brauer’s three main theorems to the π-blocks. In this paper, depending on Isaacs’ and Slattery’s work, we will extend the first main theorem for π-blocks.  相似文献   

9.
LetK be a class of spaces which are eigher a pseudo-opens-image of a metric space or ak-space having a compact-countable closedk-network. LetK′ be a class of spaces which are either a Fréchet space with a point-countablek-network or a point-G δ k-space having a compact-countablek-network. In this paper, we obtain some sufficient and necessary conditions that the products of finitely or countably many spaces in the classK orK′ are ak-space. The main results are that
Theorem A  If X, Y∈K. Then X x Y is a k-space if and only if (X, Y) has the Tanaka's condition.
Theorem B  The following are equivalent:
(a)  BF(ω 2)is false.
(b)  For each X, Y ∈ K′, X x Y is a k-space if and only if (X,Y) has the Tanaka's condition.
Project supported by the Mathematical Tianyuan Foundation of China  相似文献   

10.
If (Ω,Σ) is a measurable space and X a Banach space, we provide sufficient conditions on Σ and X in order to guarantee that bvca(Σ, X) the Banach space of all X-valued countably additive measures of bounded variation equipped with the variation norm, contains a copy of c0 if and only if X does. This work was supported by the project MTM2005-01182 of the Spanish Ministry of Education and Science, co-financed by the European Community (Feder projects).  相似文献   

11.
We make a definition of ω-precategory which should underlie any definition of weak ω-category. We make a precise definition of pseudo-invertible cells in this setting. We show that in an ω-precategory with all weak duals, every cell is pseudo-invertible. We deduce that in any “sensible” theory of ω-categories, an ω-category with all weak duals is an ω-groupoid. We discuss various examples and open questions involving higher-dimensional tangles and cobordisms.   相似文献   

12.
It is proved that ifX is a connected locally continuumwise connected coanalytic nowhere topologically complete space, then the hyperspace 2 X of all nonempty compact subsets ofX is strongly universal in the class of all coanalytic spaces. Moreover, 2 X is homeomorphic to Π2 ifX is a Baire space, and toQ∖Π1 ifX contains a dense absoluteG δ-setGX such that the intersectionGU is connected for any open connectedUX. (Here Π1, Π1X are the standard subsets of the Hilbert cubeQ absorbing for the classes of analytic and coanalytic spaces, respectively.) Similar results are obtained for higher projective classes. Translated fromMatematicheskie Zametki, Vol. 62, No. 1, pp. 35–51, July, 1997. Translated by O. V. Sipacheva  相似文献   

13.
Let X be a topological space and (Y,d) be a metric space. If f: XY is a function then there is a function a f : X → [0, ∞] such that f is almost continuous at x if and only if a f (x) = 0. Some properties of this function are investigated. Supported by grant VEGA 2/6087/26 and APVT-51-006904.  相似文献   

14.
Characterizations and Extensions of Lipschitz-α Operators   总被引:1,自引:0,他引:1  
In this work, we prove that a map F from a compact metric space K into a Banach space X over F is a Lipschitz-α operator if and only if for each σ in X^* the map σoF is a Lipschitz-α function on K. In the case that K = [a, b], we show that a map f from [a, b] into X is a Lipschitz-1 operator if and only if it is absolutely continuous and the map σ→ (σ o f)' is a bounded linear operator from X^* into L^∞([a, b]). When K is a compact subset of a finite interval (a, b) and 0 〈 α ≤ 1, we show that every Lipschitz-α operator f from K into X can be extended as a Lipschitz-α operator F from [a, b] into X with Lα(f) ≤ Lα(F) ≤ 3^1-α Lα(f). A similar extension theorem for a little Lipschitz-α operator is also obtained.  相似文献   

15.
Let X be a topological group or a convex set in a linear metric space. We prove that X is homeomorphic to (a manifold modeled on) an infinite-dimensional Hilbert space if and only if X is a completely metrizable absolute (neighborhood) retract with ω-LFAP, the countable locally finite approximation property. The latter means that for any open cover of X there is a sequence of maps (f n : XX) nεgw such that each f n is -near to the identity map of X and the family {f n (X)} nω is locally finite in X. Also we show that a metrizable space X of density dens(X) < is a Hilbert manifold if X has gw-LFAP and each closed subset AX of density dens(A) < dens(X) is a Z -set in X.   相似文献   

16.
Let (e i ) be a dictionary for a separable infinite-dimensional Banach space X. We consider the problem of approximation by linear combinations of dictionary elements with quantized coefficients drawn usually from a ‘finite alphabet’. We investigate several approximation properties of this type and connect them to the Banach space geometry of X. The existence of a total minimal system with one of these properties, namely the coefficient quantization property, is shown to be equivalent to X containing c 0. We also show that, for every ε>0, the unit ball of every separable infinite-dimensional Banach space X contains a dictionary (x i ) such that the additive group generated by (x i ) is (3+ε)−1-separated and 1/3-dense in X.   相似文献   

17.
The ℒ p spaces     
The ℒ p spaces which were introduced by A. Pełczyński and the first named author are studied. It is proved, e.g., that (i)X is an ℒ p space if and only ifX* is and ℒ q space (p −1+q −1=1). (ii) A complemented subspace of an ℒ p space is either an ℒ p or an ℒ2 space. (iii) The ℒ p spaces have sufficiently many Boolean algebras of projections. These results are applied to show thatX is an ℒ (resp. ℒ1) space if and only ifX admits extensions (resp. liftings) of compact operators havingX as a domain or range space. We also prove a theorem on the “local reflexivity” of an arbitrary Banach space. This research was partially supported by NSF Grant# 8964.  相似文献   

18.
We investigate Besov spaces and their connection with trigonometric polynomial approximation inL p[−π,π], algebraic polynomial approximation inL p[−1,1], algebraic polynomial approximation inL p(S), and entire function of exponential type approximation inL p(R), and characterizeK-functionals for certain pairs of function spaces including (L p[−π,π],B s a(L p[−π,π])), (L p(R),s a(Lp(R))), , and , where 0<s≤∞, 0<p<1,S is a simple polytope and 0<α<r. This project is supported by the National Science Foundation of China.  相似文献   

19.
LetX (Δ) be the real toric variety associated to a smooth fan Δ. The main purpose of this article is: (i) to determine the fundamental group and the universal cover ofX (Δ), (ii) to give necessary and sufficient conditions on Δ under which π1(X(Δ)) is abelian, (iii) to give necessary and sufficient conditions on Δ under whichX(Δ) is aspherical, and when Δ is complete, (iv) to give necessary and sufficient conditions forC Δ to be aK (π, 1) space whereC Δ is the complement of a real subspace arrangement associated to Δ.  相似文献   

20.
Let X be a Banach space. We show that each m : ? \ {0} → L (X ) satisfying the Mikhlin condition supx ≠0(‖m (x )‖ + ‖xm ′(x )‖) < ∞ defines a Fourier multiplier on B s p,q (?; X ) if and only if 1 < p < ∞ and X is isomorphic to a Hilbert space; each bounded measurable function m : ? → L (X ) having a uniformly bounded variation on dyadic intervals defines a Fourier multiplier on B s p,q (?; X ) if and only if 1 < p < ∞ and X is a UMD space. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)  相似文献   

设为首页 | 免责声明 | 关于勤云 | 加入收藏

Copyright©北京勤云科技发展有限公司  京ICP备09084417号