共查询到20条相似文献,搜索用时 15 毫秒
1.
Let X be a Banach space with a separable dual X*. Let ${Y\subset X}Let X be a Banach space with a separable dual X*. Let Y ì X{Y\subset X} be a closed subspace, and
f:Y?\mathbbR{f:Y\rightarrow\mathbb{R}} a C
1-smooth function. Then we show there is a C
1 extension of f to X. 相似文献
2.
M. Zippin 《Israel Journal of Mathematics》1977,26(3-4):372-387
It is proved that every infinite dimensional separable Banach space having the separable extension property is isomorphic to c0. It is also proved that every Banach space with a separable dual is “close” to a space of continuous functions on a countable compact space. 相似文献
3.
Dale E Alspach 《Journal of Functional Analysis》1982,45(2):139-168
Let T be a bounded linear operator from a separable Banach space X to a Banach space Y. A necessary and sufficient condition on T for the existence of a subspace Z of X such that Z is isomorphic to C(α) and the restriction of T to Z is an isomorphism is given. The special case where X is the disc algebra is then considered and results similar to those previously obtained by the author for C(K) spaces are obtained for the disc algebra. Finally some additional results of the same type are proved for subspaces of C(K) with small annihilator. 相似文献
4.
A. S. Kravchenko 《Siberian Mathematical Journal》2006,47(1):68-76
We consider the space M(X) of separable measures on the Borel σ-algebra ?(X) of a metric space X. The space M(X) is furnished with the Kantorovich-Rubinshtein metric known also as the “Hutchinson distance” (see [1]). We prove that M(X) is complete if and only if X is complete. We consider applications of this theorem in the theory of selfsimilar fractals. 相似文献
5.
J. Schleischitz 《Acta Mathematica Hungarica》2018,154(2):362-377
For a Tychonoff space X, we denote by C p (X) the space of all real-valued continuous functions on X with the topology of pointwise convergence.
In this paper we prove that:
相似文献
- If every finite power of X is Lindelöf then C p (X) is strongly sequentially separable iff X is \({\gamma}\)-set.
- \({B_{\alpha}(X)}\) (= functions of Baire class \({\alpha}\) (\({1 < \alpha \leq \omega_1}\)) on a Tychonoff space X with the pointwise topology) is sequentially separable iff there exists a Baire isomorphism class \({\alpha}\) from a space X onto a \({\sigma}\)-set.
- \({B_{\alpha}(X)}\) is strongly sequentially separable iff \({iw(X)=\aleph_0}\) and X is a \({Z^{\alpha}}\)-cover \({\gamma}\)-set for \({0 < \alpha \leq \omega_1}\).
- There is a consistent example of a set of reals X such that C p (X) is strongly sequentially separable but B1(X) is not strongly sequentially separable.
- B(X) is sequentially separable but is not strongly sequentially separable for a \({\mathfrak{b}}\)-Sierpiński set X.
6.
A space X is said to be selectively separable (=M-separable) if for each sequence {Dn:n∈ω} of dense subsets of X, there are finite sets Fn⊂Dn (n∈ω) such that ?{Fn:n∈ω} is dense in X. On selective separability and its variations, we show the following: (1) Selective separability, R-separability and GN-separability are preserved under finite unions; (2) Assuming CH (the continuum hypothesis), there is a countable regular maximal R-separable space X such that X2 is not selectively separable; (3) c{0,1} has a selectively separable, countable and dense subset S such that the group generated by S is not selectively separable. These answer some questions posed in Bella et al. (2008) [7]. 相似文献
7.
We give a unified method to obtain the conservativeness of a class of Markov processes associated with lower bounded semi-Dirichlet forms on L 2(X;m), including symmetric diffusion processes, some non-symmetric diffusion processes and jump type Markov processes on X, where X is a locally compact separable metric space and m is a positive Radon measure on X with full topological support. Using the method, we give an example in each section, providing the conservativeness of the processes, that are given by the “increasingness of the volume of some sets(balls)” and “that of the coefficients on the sets” of the Markov processes. 相似文献
8.
It is shown that for compact metric spaces (X, d) the following statements are pairwise equivalent: “X is Loeb”, “X is separable”, “X has a we ordered dense subset”, “X is second countable”, and “X has a dense set G = ∪{Gn : n ∈ ω}, ∣Gn∣ < ω, with limn→∞ diam (G n) = 0”. Further, it is shown that the statement: “Compact metric spaces are weakly Loeb” is not provable in ZF0 , the Zermelo‐Fraenkel set theory without the axiom of regularity, and that the countable axiom of choice for families of finite sets CACfin does not imply the statement “Compact metric spaces are separable”. 相似文献
9.
10.
Frame expansions in separable Banach spaces 总被引:2,自引:0,他引:2
Banach frames are defined by straightforward generalization of (Hilbert space) frames. We characterize Banach frames (and Xd-frames) in separable Banach spaces, and relate them to series expansions in Banach spaces. In particular, our results show that we can not expect Banach frames to share all the nice properties of frames in Hilbert spaces. 相似文献
11.
R.H. Marty 《Topology and its Applications》1982,14(3):305-311
Let X denote the product of m-many second countable Hausdorff spaces. Main theorems: (1) If S?X is invariant under compositions, m is weakly accessible (resp., nonmeasurable), and F?S is sequentially closed and a sequential Gσ-set which is invariant under projections for finite sets (resp., F?S is sequentially open and sequentially closed), then F is closed. (2) If S?X is invariant under projections and m is nonmeasurable, then every sequentially continuous {0, 1} valued function on S is continuous. (3) A sequentially continuous {0, 1}-valued function on an m-adic space of nonmeasurable weight is continuous. Now let X denote the product of arbitrarily many W-spaces and S?X be invariant under compositions. (4) Then in S, the closure of any Q-open subset coincides with its sequential closure. 相似文献
12.
《Quaestiones Mathematicae》2013,36(4):535-548
Abstract Given a topological abelian group G, we study the class of strongly sequentially continuous functions on G. Strong sequential continuity is a property intermediate between sequential continuity and uniform sequential continuity, which appeared naturally in the study of smooth functions on Banach spaces. In this paper, we shall mainly concentrate on the gap between strong sequential continuity and uniform sequential continuity. It turns out that if G has some completeness property—for example, if it is completely metrizable—then all strongly sequentially continuous functions on G are uniformly sequentially continuous. On the other hand, we exhibit a large and natural class of groups for which the two notions differ. This class is defined by a property reminiscent of the classical Dirichlet theorem; it includes all dense sugroups of R generated by an increasing sequence of Dirichlet sets, and groups of the form (X, w), where X is a separable Banach space failing the Schur property. Finally, we show that the family of bounded, real-valued strongly sequentially continuous functions on G is a closed subalgebra of l∞(G). 相似文献
13.
Joram Lindenstrauss 《Israel Journal of Mathematics》1971,9(3):279-284
For every separable Banach spaceX there is a Banach spaceY with a separable dual such thatY ⊕X* ≈Y**. There is also a separable spaceZ so thatZ**/JZ is isomorphic toX. 相似文献
14.
G.A Edgar 《Journal of Functional Analysis》1976,23(2):145-161
Let X be a closed bounded convex subset with the Radon-Nikodym property of a Banach space. For tight Borel probability measures μ, v on X, define μ ? v iff there is a dilation T on X such that T(μ) = v. Then, for every x?X, there is a measure μ on X which is maximal in the partial order ? and which has barycenter x. If X is separable, then μ(ex X) = 1 for all maximal measures μ. In general, a maximal measure need not be “on” ex X in this strong sense. If X is weakly compact, then a maximal measure is “on” ex X in the looser sense that μ(B) = 1 for all weak Baire sets B ? ex X. 相似文献
15.
16.
Jonathan K. Hodge 《Discrete Applied Mathematics》2006,154(10):1478-1499
The notion of separability is important in economics, operations research, and political science, where it has recently been studied within the context of referendum elections. In a referendum election on n questions, a voter's preferences may be represented by a linear order on the 2n possible election outcomes. The symmetric group of degree 2n, S2n, acts in a natural way on the set of all such linear orders. A permutation σ∈S2n is said to preserve separability if for each separable order ?, σ(?) is also separable. Here, we show that the set of separability-preserving permutations is a subgroup of S2n and, for 4 or more questions, is isomorphic to the Klein 4-group. Our results indicate that separable preferences are rare and highly sensitive to small changes. The techniques we use have applications to the problem of enumerating separable preference orders and to other broader combinatorial questions. 相似文献
17.
Liang-Xue Peng 《Topology and its Applications》2007,154(11):2223-2227
It is shown that if X is a countably compact space that is the union of a countable family of D-spaces, then X is compact. This gives a positive answer to Arhangel'skii's problem [A.V. Arhangel'skii, D-spaces and finite unions, Proc. Amer. Math. Soc. 132 (7) (2004) 2163-2170]. In this note, we also obtain a result that if a regular space X is sequential and has a point-countable k-network, then X is a D-space. 相似文献
18.
Marius Dadarlat 《Advances in Mathematics》2009,222(5):1850-2880
Let X be a finite dimensional compact metrizable space. We study a technique which employs semiprojectivity as a tool to produce approximations of C(X)-algebras by C(X)-subalgebras with controlled complexity. The following applications are given. All unital separable continuous fields of C*-algebras over X with fibers isomorphic to a fixed Cuntz algebra On, n∈{2,3,…,∞}, are locally trivial. They are trivial if n=2 or n=∞. For n?3 finite, such a field is trivial if and only if (n−1)[A1]=0 in K0(A), where A is the C*-algebra of continuous sections of the field. We give a complete list of the Kirchberg algebras D satisfying the UCT and having finitely generated K-theory groups for which every unital separable continuous field over X with fibers isomorphic to D is automatically locally trivial or trivial. In a more general context, we show that a separable unital continuous field over X with fibers isomorphic to a KK-semiprojective Kirchberg C*-algebra is trivial if and only if it satisfies a K-theoretical Fell type condition. 相似文献
19.
Vitalij A. Chatyrko 《Topology and its Applications》2005,152(3):269-274
For each pair of positive integers k and m with k?m there exists a separable metrizable space X(k,m) such that cmpX(k,m)=k and defX(k,m)=m. This solves Problem 6 from [J.M. Aarts, T. Nishiura, Dimension and Extensions, North-Holland, Amsterdam, 1993, p. 71]. 相似文献
20.
José Rodríguez 《Archiv der Mathematik》2007,88(1):62-70
Let X be a weakly Lindel?f determined Banach space. We prove that the following two statements are equivalent:
Some applications and related examples are given.
Received: 11 January 2006; Revised: 24 May 2006 相似文献
(i) | Every Radon probability measure on (BX*, w*) has separable support. |
(ii) | Every countably additive X*-valued measure with σ-finite variation has norm separable range. |