共查询到20条相似文献,搜索用时 453 毫秒
1.
We formulate a general theory of positions for subspaces of a Banach space: we define equivalent and isomorphic positions, study the automorphy index a(Y,X) that measures how many non-equivalent positions Y admits in X, and obtain estimates of a(Y,X) for X a classical Banach space such as ?p,Lp,L1,C(ωω) or C[0,1]. Then, we study different aspects of the automorphic space problem posed by Lindenstrauss and Rosenthal; namely, does there exist a separable automorphic space different from c0 or ?2? Recall that a Banach space X is said to be automorphic if every subspace Y admits only one position in X; i.e., a(Y,X)=1 for every subspace Y of X. We study the notion of extensible space and uniformly finitely extensible space (UFO), which are relevant since every automorphic space is extensible and every extensible space is UFO. We obtain a dichotomy theorem: Every UFO must be either an L∞-space or a weak type 2 near-Hilbert space with the Maurey projection property. We show that a Banach space all of whose subspaces are UFO (called hereditarily UFO spaces) must be asymptotically Hilbertian; while a Banach space for which both X and X∗ are UFO must be weak Hilbert. We then refine the dichotomy theorem for Banach spaces with some additional structure. In particular, we show that an UFO with unconditional basis must be either c0 or a superreflexive weak type 2 space; that a hereditarily UFO Köthe function space must be Hilbert; and that a rearrangement invariant space UFO must be either L∞ or a superreflexive type 2 Banach lattice. 相似文献
2.
Jie-Hua Mai 《Topology and its Applications》2011,158(16):2216-2220
Let X be a topological space, f:X→X be a continuous map, and Y be a compact, connected and closed subset of X. In this paper we show that, if the boundary X∂Y contains exactly one point v and f(v)∈Y, then Y contains a minimal set of f. 相似文献
3.
Risong Li 《Communications in Nonlinear Science & Numerical Simulation》2012,17(7):2815-2823
Let f : X → X be a continuous map of a compact metric space X. The map f induces in a natural way a map fM on the space M(X) of probability measures on X, and a transformation fK on the space K(X) of closed subsets of X. In this paper, we show that if (X, f) is a chain transitive system with shadowing property, then exactly one of the following two statements holds:
- (a)
- fn and (fK)n are syndetically sensitive for all n ? 1.
- (b)
- fn and (fK)n are equicontinuous for all n ? 1.
4.
William B. JohnsonJoram Lindenstrauss David PreissGideon Schechtman 《Journal of Functional Analysis》2002,194(2):332-346
If X is any separable Banach space containing l1, then there is a Lipschitz quotient map from X onto any separable Banach space Y. 相似文献
5.
Marta Štefánková 《Topology and its Applications》2006,153(14):2673-2679
In the paper of Alsedà, Kolyada, Llibre and Snoha [L. Alsedà, S.F. Kolyada, J. Llibre, L'. Snoha, Entropy and periodic points for transitive maps, Trans. Amer. Math. Soc. 351 (1999) 1551-1573] there was—among others—proved that a nonminimal continuous transitive map f of a compact metric space (X,ρ) can be extended to a triangular map F on X×I (i.e., f is the base for F) in such a way that F is transitive and has the same entropy as f. The presented paper shows that under certain conditions the extension of minimal maps is guaranteed, too: Let (X,f) be a solenoidal dynamical system. Then there exist a transitive triangular map F such that h(F)=h(f). 相似文献
6.
Francis Jordan 《Topology and its Applications》2010,157(15):2392-1968
Let C(X,Y) be the set of all continuous functions from a topological space X into a topological space Y. We find conditions on X that make the Isbell and fine Isbell topologies on C(X,Y) equal for all Y. For zero-dimensional spaces X, we show there is a space Z such that the coincidence of the Isbell and fine Isbell topologies on C(X,Z) implies the coincidence on C(X,Y) for all Y. We then consider the question of when the Isbell and fine Isbell topologies coincide on the set of continuous real-valued functions. Our results are similar to results established for consonant spaces. 相似文献
7.
Let (X, d) be a compact metric space and fn : X → X a sequence of continuous maps such that (fn) converges uniformly to a map f. The purpose of this paper is to study the Devaney’s chaos on the uniform limit f. On the one hand, we show that f is not necessarily transitive even if all fn mixing, and the sensitive dependence on initial conditions may not been inherited to f even if the iterates of the sequence have some uniform convergence, which correct two wrong claims in [1]. On the other hand, we give some equivalence conditions for the uniform limit f to be transitive and to have sensitive dependence on initial conditions. Moreover, we present an example to show that a non-transitive sequence may converge uniformly to a transitive map. 相似文献
8.
Zahava Shmuely 《Journal of Combinatorial Theory, Series A》1976,21(3):369-383
The (isotone) map f: X → X is an increasing (decreasing) operator on the poset X if f(x) ? f2(x) (f2(x) ? f(x), resp.) holds for each x ∈ X. Properties of increasing (decreasing) operators on complete lattices are studied and shown to extend and clarify those of closure (resp. anticlosure) operators. The notion of the decreasing closure, , (the increasing anticlosure, ,) of the map f: X → X is introduced extending that of the transitive closure, , of f. , and are all shown to have the same set of fixed points. Our results enable us to solve some problems raised by H. Crapo. In particular, the order structure of H(X), the set of retraction operators on X is analyzed. For X a complete lattice H(X) is shown to be a complete lattice in the pointwise partial order. We conclude by claiming that it is the increasing-decreasing character of the identity maps which yields the peculiar properties of Galois connections. This is done by defining a u-v connection between the posets X and Y, where u: X → X (v: Y → Y) is an increasing (resp. decreasing) operator to be a pair f, g of maps f; X → Y, g: Y → X such that gf ? u, fg ? v. It is shown that the whole theory of Galois connections can be carried over to u-v connections. 相似文献
9.
Dr. J. Globevnik 《Monatshefte für Mathematik》1975,79(4):299-301
LetD be a subset of a complex linear spaceL such that for everyu∈D,v∈L the setΩ(u, v) = {ζ∣u+ζv∈D} is an open connected set in the complex plane. Denote byA (D, X) the linear space of allG-analytic mappings fromD to a complex Hilbert spaceX.Theorem: LetZ be a complex linear space and letA, B be linear operators fromZ toA (D, X), A (D, Y), respectively, whereX, Y are complex Hilbert spaces. If ∥(A p)u∥ X =∥(B p)u∥ Y (p∈Z,u∈D) then a maximal partial isometryW:X→Y exists such that(Bp)u=W((Ap)u) (p∈Z, u∈D). 相似文献
10.
《Quaestiones Mathematicae》2013,36(3-4):269-288
Abstract Using a lifting of £∞ (μ, X) ([5],[6]), we construct a lifting ρ x of the seminormed vector space £∞ (μ, X) of measurable, essentially bounded X-valued functions. We show that in a certain sense such a lifting always exists. If μ is Lebesgue measure on (0, 1) we show that ρ x exists as map from £∞ ((O, 1), X) → £∞,((0, l), X) if and only if X is reflexive. In general the lifted function takes its values in X **. Therefore we investigate the question, when f ε £∞ (μ, X) is strictly liftable in the sense that the lifted function is a map with values even in X. As an application we introduce the space £∞ strong (μ, L (X, Y**)), a subspace of the space of strongly measurable, essentially bounded L (X, Y, **)-valued functions, and the associated quotient space £∞ strong (μ, L (X,Y**)). We show that this space is a Banach space because there is a kind of a Dunford-Pettis Theorem for a subspace of L (X, £∞(μ Y**)). Finally we investigate the measurability property of functions in £∞(μ Y**)) und see that there exists a connection to the Radon-Nikodym property of the space L (X, Y). 相似文献
11.
Haruto Ohta 《Topology and its Applications》1984,17(3):265-274
In response to questions of Ginsburg [9, 10], we prove that if cf(c)>ω1, then there exists an open-closed, continuous map f from a normal, realcompact space X onto a space Y which is not realcompact. By his result the hyperspace 2x of closed subsets of X is then not realcompact, and the extension μf(vf) of f to the topological completion (the Hewitt realcompactification) of X is not onto. The latter fact solves problems raised by Morita [16] and by Isiwata [12] both negatively. We also consider the problem whether or not the hyperspace of a hereditarily Lindelöf space is hereditarily realcompact. 相似文献
12.
Let X and Y be superreflexive complex Banach spaces and let B(X) and B(Y) be the Banach algebras of all bounded linear operators on X and Y, respectively. If a bijective linear map Φ:B(X)→B(Y) almost preserves the spectra, then it is almost multiplicative or anti-multiplicative. Furthermore, in the case where X=Y is a separable complex Hilbert space, such a map is a small perturbation of an automorphism or an anti-automorphism. 相似文献
13.
Shin-Yao Jow 《Mathematische Zeitschrift》2011,268(1-2):197-209
Let X be a smooth Mori dream space of dimension ?? 4. We show that, if X satisfies a suitable GIT condition which we call small unstable locus, then every smooth ample divisor Y of X is also a Mori dream space. Moreover, the restriction map identifies the Néron?CSeveri spaces of X and Y, and under this identification every Mori chamber of Y is a union of some Mori chambers of X, and the nef cone of Y is the same as the nef cone of X. This Lefschetz-type theorem enables one to construct many examples of Mori dream spaces by taking ??Mori dream hypersurfaces?? of an ambient Mori dream space, provided that it satisfies the GIT condition. To facilitate this, we then show that the GIT condition is stable under taking products and taking the projective bundle of the direct sum of at least three line bundles, and in the case when X is toric, we show that the condition is equivalent to the fan of X being 2-neighborly. 相似文献
14.
To every Poisson algebraic variety X over an algebraically closed field of characteristic zero, we canonically attach a right D-module M(X) on X. If X is affine, solutions of M(X) in the space of algebraic distributions on X are Poisson traces on X, i.e. distributions invariant under Hamiltonian flow. When X has finitely many symplectic leaves, we prove that M(X) is holonomic. Thus, when X is affine and has finitely many symplectic leaves, the space of Poisson traces on X is finite-dimensional. More generally, to any morphism ${\phi : X \to Y}To every Poisson algebraic variety X over an algebraically closed field of characteristic zero, we canonically attach a right D-module M(X) on X. If X is affine, solutions of M(X) in the space of algebraic distributions on X are Poisson traces on X, i.e. distributions invariant under Hamiltonian flow. When X has finitely many symplectic leaves, we prove that M(X) is holonomic. Thus, when X is affine and has finitely many symplectic leaves, the space of Poisson traces on X is finite-dimensional. More generally, to any morphism f: X ? Y{\phi : X \to Y} and any quasicoherent sheaf of Poisson modules N on X, we attach a right D-module Mf(X,N){M_\phi(X,N)} on X, and prove that it is holonomic if X has finitely many symplectic leaves, f{\phi} is finite, and N is coherent. 相似文献
15.
Jian Li 《Topology and its Applications》2011,158(16):2221-2231
Let (X,T) be a topological dynamical system and F be a Furstenberg family (a collection of subsets of Z+ with hereditary upward property). A point x∈X is called an F-transitive one if {n∈Z+:Tnx∈U}∈F for every non-empty open subset U of X; the system (X,T) is called F-point transitive if there exists some F-transitive point. In this paper, we aim to classify transitive systems by F-point transitivity. Among other things, it is shown that (X,T) is a weakly mixing E-system (resp. weakly mixing M-system, HY-system) if and only if it is {D-sets}-point transitive (resp. {central sets}-point transitive, {weakly thick sets}-point transitive).It is shown that every weakly mixing system is Fip-point transitive, while we construct an Fip-point transitive system which is not weakly mixing. As applications, we show that every transitive system with dense small periodic sets is disjoint from every totally minimal system and a system is Δ?(Fwt)-transitive if and only if it is weakly disjoint from every P-system. 相似文献
16.
A function J defined on a family C of stationary processes is finitely observable if there is a sequence of functions s
n
such that s
n
(x
1,…, x
n
) → J(X) in probability for every process X=(x
n
) ∈ C. Recently, Ornstein and Weiss proved the striking result that if C is the class of aperiodic ergodic finite valued processes, then the only finitely observable isomorphism invariant defined
on C is entropy [8]. We sharpen this in several ways. Our main result is that if X → Y is a zero-entropy extension of finite entropy ergodic systems and C is the family of processes arising from generating partitions of X and Y, then every finitely observable function on C is constant. This implies Ornstein and Weiss’ result, and extends it to many other families of processes, e.g., it follows
that there are no nontrivial finitely observable isomorphism invariants for processes arising from the class of Kronecker
systems, the class of mild mixing zero entropy systems, or the class of strong mixing zero entropy systems. It also follows
that for the class of processes arising from irrational rotations, every finitely observable isomorphism invariant must be
constant for rotations belonging to a set of full Lebesgue measure.
This research was supported by the Israel Science Foundation (grant No. 1333/04) 相似文献
17.
Yevhen Zelenyuk 《Topology and its Applications》2007,154(2):339-357
A topological space X is called almost maximal if it is without isolated points and for every x∈X, there are only finitely many ultrafilters on X converging to x. We associate with every countable regular homogeneous almost maximal space X a finite semigroup Ult(X) so that if X and Y are homeomorphic, Ult(X) and Ult(Y) are isomorphic. Semigroups Ult(X) are projectives in the category F of finite semigroups. These are bands decomposing into a certain chain of rectangular components. Under MA, for each projective S in F, there is a countable almost maximal topological group G with Ult(G) isomorphic to S. The existence of a countable almost maximal topological group cannot be established in ZFC. However, there are in ZFC countable regular homogeneous almost maximal spaces X with Ult(X) being a chain of idempotents. 相似文献
18.
Dongyang Chen 《Journal of Mathematical Analysis and Applications》2003,284(2):618-625
If X is a separable Banach space, then X∗ contains an asymptotically isometric copy of l1 if and only if there exists a quotient space of X which is asymptotically isometric to c0. If X is an infinite-dimensional normed linear space and Y is any Banach space containing an asymptotically isometric copy of c0, then L(X,Y) contains an isometric copy of l∞. If X and Y are two infinite-dimensional Banach spaces and Y contains an asymptotically isometric copy of c0, then contains a complemented asymptotically isometric copy of c0. 相似文献
19.
M.R. Koushesh 《Topology and its Applications》2007,154(14):2607-2634
If a Tychonoff space X is dense in a Tychonoff space Y, then Y is called a Tychonoff extension of X. Two Tychonoff extensions Y1 and Y2 of X are said to be equivalent, if there exists a homeomorphism which keeps X pointwise fixed. This defines an equivalence relation on the class of all Tychonoff extensions of X. We identify those extensions of X which belong to the same equivalence classes. For two Tychonoff extensions Y1 and Y2 of X, we write Y2?Y1, if there exists a continuous function which keeps X pointwise fixed. This is a partial order on the set of all (equivalence classes of) Tychonoff extensions of X. If a Tychonoff extension Y of X is such that Y\X is a singleton, then Y is called a one-point extension of X. Let T(X) denote the set of all one-point extensions of X. Our purpose is to study the order structure of the partially ordered set (T(X),?). For a locally compact space X, we define an order-anti-isomorphism from T(X) onto the set of all nonempty closed subsets of βX\X. We consider various sets of one-point extensions, including the set of all one-point locally compact extensions of X, the set of all one-point Lindelöf extensions of X, the set of all one-point pseudocompact extensions of X, and the set of all one-point ?ech-complete extensions of X, among others. We study how these sets of one-point extensions are related, and investigate the relation between their order structure, and the topology of subspaces of βX\X. We find some lower bounds for cardinalities of some of these sets of one-point extensions, and in a concluding section, we show how some of our results may be applied to obtain relations between the order structure of certain subfamilies of ideals of C∗(X), partially ordered with inclusion, and the topology of subspaces of βX\X. We leave some problems open. 相似文献
20.
Takefumi Nosaka 《Topology and its Applications》2011,158(8):996-1011
For a quandle X, the quandle space BX is defined, modifying the rack space of Fenn, Rourke and Sanderson (1995) [13], and the quandle homotopy invariant of links is defined in Z[π2(BX)], modifying the rack homotopy invariant of Fenn, Rourke and Sanderson (1995) [13]. It is known that the cocycle invariants introduced in Carter et al. (2005) [3], Carter et al. (2003) [5], Carter et al. (2001) [6] can be derived from the quandle homotopy invariant.In this paper, we show that, for a finite quandle X, π2(BX) is finitely generated, and that, for a connected finite quandle X, π2(BX) is finite. It follows that the space spanned by cocycle invariants for a finite quandle is finitely generated. Further, we calculate π2(BX) for some concrete quandles. From the calculation, all cocycle invariants for those quandles are concretely presented. Moreover, we show formulas of the quandle homotopy invariant for connected sum of knots and for the mirror image of links. 相似文献