共查询到20条相似文献,搜索用时 31 毫秒
1.
Jacques Stern 《Israel Journal of Mathematics》1976,24(1):1-15
LetX be a Banach space. A Banach spaceY is an envelope ofX if (1)Y is finitely representable inX; (2) any Banach spaceZ finitely representable inX and of density character not exceeding that ofY is isometric to a subspace ofY. Lindenstrauss and Pelczynski have asked whether any separable Banach space has a separable envelope. We give a negative
answer to this question by showing the existence of a Banach space isomorphic tol
2, which has no separable envelope. A weaker positive result holds: any separable Banach space has an envelope of density character
≦ℵ1 (assuming the continuum hypothesis). 相似文献
2.
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
3.
Wang Yangeng 《数学学报(英文版)》1997,13(3):333-336
The space of continuous maps from a topological spaceX to topological spaceY is denoted byC(X,Y) with the compact-open topology. In this paper we prove thatC(X,Y) is an absolute retract ifX is a locally compact separable metric space andY a convex set in a Banach space. From the above fact we know thatC(X,Y) is homomorphic to Hilbert spacel
2 ifX is a locally compact separable metric space andY a separable Banach space; in particular,C(R
n,Rm) is homomorphic to Hilbert spacel
2.
This research is supported by the Science Foundation of Shanxi Province's Scientific Committee 相似文献
4.
Given a compact metric space X and a continuous map f from X to itself, we construct a barrier function for chain-recurrence. We use it to endow the space of chain-transitive components with a non-trivial ultrametric distance and to construct Lyapunov functions for f. Most of these constructions are then generalized on an arbitrary separable metric space to a continuous compactum-valued map. 相似文献
5.
Multidimensional ultrametric pseudodifferential equations 总被引:1,自引:1,他引:0
We develop an analysis of wavelets and pseudodifferential operators on multidimensional ultrametric spaces which are defined
as products of locally compact ultrametric spaces. We introduce bases of wavelets, spaces of generalized functions and the
space D′0(X) of generalized functions on a multidimensional ultrametric space. We also consider some family of pseudodifferential operators
on multidimensional ultrametric spaces. The notions of Cauchy problem for ultrametric pseudodifferential equations and of
ultrametric characteristics are introduced. We prove an existence theorem and describe all solutions for the Cauchy problem
(an analog of the Kovalevskaya theorem). 相似文献
6.
Given a separable Orlicz sequence spacel
F we investigate those Orlicz sequence spacesl
f which are isomorphic to subspaces (respectively complemented subspaces) ofl
F. We give in particular an example of a reflexive Orlicz sequence space which does not contain anyl
p, 1<p<∞, as a complemented subspace. 相似文献
7.
《Quaestiones Mathematicae》2013,36(2):235-240
We give various constructions of which the most significant is a continuous scalar-valued 2-polynomial W on the separable Hilbert space l 2 and an unbounded set R ? l 2 such that (i) W is bounded on an ?-neighbourhood of R; (ii) W is unbounded on ½R; (iii) W does not factor through any (continuous or not) 1-polynomial mapping from l 2 to a normed space and sending R to a bounded set. This answers in the negative two 1935 questions asked by Mazur (Problems 55 and 75 in the Scottish Book). The construction is valid both over the real and complex fields. (In finite dimensions, the questions were answered in the positive by Auerbach soon after being asked.) 相似文献
8.
A Banach space has property (S) if every normalized weakly null sequence contains a subsequences equivalent to the unit vector basis ofc
0. We show that the equivalence constant can be chosen “uniformly”, i.e., independent of the choice of the normalized weakly
null sequence. Furthermore we show that a Banach space with property (S) has property (u). This solves in the negative the conjecture that a separable Banach space with property (u) not containingl
1 has a separable dual.
This is part of this author's Ph.D. dissertation prepared at The University of Texas at Austin under the supervision of H.
P. Rosenthal. 相似文献
9.
Banach spaces X whose duals are isomorphic or isometric to l1(Γ) are characterized by certain classes of operators on X. It is proved that a separable, conjugate space isomorphic to a complemented subspace of an L1(S, Σ, μ) space is isomorphic to l1; a 1 space contained in a separable, conjugate space is isomorphic to a subspace of l1. 相似文献
10.
This paper deals with a stochastic optimization problem when its decision parameter belongs to a separable Banach space. Conditions under which strong consistency of the parameter empirical estimates holds, are established. Leastl
1-norm estimates for two models (nonlinear and nonparametric regression) are investigated as special cases of such empirical estimates. 相似文献
11.
J. Semple 《Journal of Optimization Theory and Applications》1996,88(3):743-749
This note generalizes the results of Benson, Smith, Schochetman, and Bean (Ref. 1) regarding the minimization of a positive-definite functional over the countable intersection of closed convex sets in a Hilbert space. A finite approximating subproblem for the general case is shown to have the same strong convergence properties of the earlier work without any of the specialized structures imposed therein. In particular, the current development does not rely on any properties ofl
2 and does not require the Hilbert space to be separable. 相似文献
12.
《Quaestiones Mathematicae》2013,36(3):241-249
Abstract Given any ultrametric space X and an infinitesimal (or non-standard) hull ? over an X1-saturated non-standard model of X, we prove that there is a minimal spherically complete space between X and ?. 相似文献
13.
Dhurjati Prasad Datta Santanu Raut Anuja Raychoudhuri 《P-Adic Numbers, Ultrametric Analysis, and Applications》2011,3(1):7-22
A class of ultrametric Cantor sets (C, d
u
) introduced recently (S. Raut and D. P. Datta, Fractals 17, 45–52 (2009)) is shown to enjoy some novel properties. The ultrametric d
u
is defined using the concept of relative infinitesimals and an inversion rule. The associated (infinitesimal) valuation which turns out to be both scale and reparametrization invariant, is identified
with the Cantor function associated with a Cantor set $
\tilde C
$
\tilde C
, where the relative infinitesimals are supposed to live in. These ultrametrics are both metrically as well as topologically
inequivalent compared to the topology induced by the usual metric. Every point of the original Cantor set C is identified with the closure of the set of gaps of $
\tilde C
$
\tilde C
. The increments on such an ultrametric space is accomplished by following the inversion rule. As a consequence, Cantor functions
are reinterpreted as locally constant functions on these extended ultrametric spaces. An interesting phenomenon, called growth of measure, is studied on such an ultrametric space. Using the reparametrization invariance of the valuation it is shown how the scale
factors of a Lebesgue measure zero Cantor set might get deformed leading to a deformed Cantor set with a positive measure. The definition of a new valuated exponent is introduced which is shown to yield the fatness exponent in the case of a positive measure (fat) Cantor set. However, the
valuated exponent can also be used to distinguish Cantor sets with identical Hausdorff dimension and thickness. A class of
Cantor sets with Hausdorff dimension log3 2 and thickness 1 are constructed explicitly. 相似文献
14.
Theorem 1. LetX be a Banach space. (a) IfX
∗ has a closed subspace in which no normalized sequence converges weak∗ to zero, thenl
1 is isomorphic to a subspace ofX. (b) IfX
∗ contains a bounded sequence which has no weak∗ convergent subsequence, thenX contains a separable subspace whose dual is not separable.
The second-named author was supported in part by NSF-MPS 72-04634-A03. 相似文献
15.
Mauricio Chacón-Tirado 《Topology and its Applications》2010,157(18):2769-2777
In this paper we show that the space of selections of a smooth fan is a complete separable absolute retract. Then, we show that it is homeomorphic to the Hilbert space l2. 相似文献
16.
S. J. Dilworth 《Israel Journal of Mathematics》1985,52(1-2):15-27
Suppose that 1<p≦2, 2≦q<∞. The formal identity operatorI:l
p→l
qfactorizes through any given non-compact operator from ap-smooth Banach space into aq-convex Banach space. It follows that ifX is a 2-convex space andY is an infinite dimensional subspace ofX which is isomorphic to a Hilbert space, thenY contains an isomorphic copy ofl
2 which is complemented inX. 相似文献
17.
In the short note of 1927, Urysohn constructed the metric space R that is nowhere locally separable. There is no publication with indications that R is a (noncomplete) ?-tree that has valency c at each point. The author in 1989, as well as Polterovich and Shnirelman in 1997, constructed ?-trees isometric to R unaware of the paper by Urysohn. In this paper the author considers various constructions of the ?-tree R and of the minimal complete ?-tree of valency c including R, as well as the characterizations of ?-trees, their properties, and connections with ultrametric spaces.
相似文献18.
Denny H. Leung 《Israel Journal of Mathematics》1994,87(1-3):117-128
A Banach space is polyhedral if the unit ball of each of its finite dimensional subspaces is a polyhedron. It is known that
a polyhedral Banach space has a separable dual and isc
0-saturated, i.e., each closed infinite dimensional subspace contains an isomorph ofc
0. In this paper, we show that the Orlicz sequence spaceh
M is isomorphic to a polyhedral Banach space if lim
t→0
M(Kt)/M(t)=∞ for someK<∞. We also construct an Orlicz sequence spaceh
M which isc
0-saturated, but which is not isomorphic to any polyhedral Banach space. This shows that beingc
0-saturated and having a separable dual are not sufficient for a Banach space to be isomorphic to a polyhedral Banach space. 相似文献
19.
Aldo J. Lazar 《Israel Journal of Mathematics》1975,20(3-4):369-374
Every uncountable complete separable metric space is homomorphic to the set of extreme points (in the weak topology) of a bounded closed convex body inl 2. 相似文献
20.
Joseph Y. T. Woo 《Israel Journal of Mathematics》1975,20(3-4):193-215
The class of all subspaces of quotient spaces ofl
p ⊕l, contains all separable Orlicz sequence spaces.
This is part of the author’s Ph.D. thesis prepared at University of California at Berkeley under the supervision of Professor
H. P. Rosenthal. 相似文献