共查询到20条相似文献,搜索用时 93 毫秒
1.
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
2.
Yves Raynaud 《Israel Journal of Mathematics》1989,65(2):197-213
We show that ifl
p(X),p ≠ 2, is finitely crudely representable in an Orlicz spaceL
ϕ (which does not containc
0) then the Banach spaceX is isomorphic to a subspace ofL
p. The same remains true forp = 2 whenL
ϕ is 2-concave or 2-convex, or ifX has local unconditional structure. We extend a theorem of Guerre and Levy to Orlicz function spaces. 相似文献
3.
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
4.
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
5.
In every ∞-dimensional separable Banach spaceX there is a fundamental sequence such that no subsequence of it, which is fundamental inX, is independent (“{x
n} is fundamental inX” meansX=span {x
n}). 相似文献
6.
C. J. Read 《Israel Journal of Mathematics》1987,57(3):375-380
In our earlier paper [1] we showed that given any elementx of a commutative unital Banach algebraA, there is an extensionA′ ofA such that the spectrum ofx inA′ is precisely the essential spectrum ofx inA. In [2], we showed further that ifT is a continuous linear operator on a Banach spaceX, then there is an extensionY ofX such thatT extends continuously to an operatorT
− onY, and the spectrum ofT
− is precisely the approximate point spectrum ofT. In this paper we take the second of these results, and show further that ifX is a Hilbert space then we can ensure thatY is also a Hilbert space; so any operatorT on a Hilbert spaceX is the restriction to one copy ofX of an operatorT
− onX ⊕X, whose spectrum is precisely the approximate point spectrum ofT. This result is “best possible” in the sense that if
isany extension to a larger Banach space of an operatorT, it is a standard exercise that the approximate point spectrum ofT is contained in the spectrum of
. 相似文献
7.
S. M. Bates 《Israel Journal of Mathematics》1997,100(1):209-220
It is shown that (1) every infinite-dimensional Banach space admits aC
1 Lipschitz map onto any separable Banach space, and (2) if the dual of a separable Banach spaceX contains a normalized, weakly null Banach-Saks sequence, thenX admits aC
∞ map onto any separable Banach space. Subsequently, we generalize these results to mappings onto larger target spaces.
Supported by an NSF Postdoctoral Fellowship in Mathematics. 相似文献
8.
P. Mankiewicz 《Israel Journal of Mathematics》1989,65(1):1-16
A separable superreflexive Banach spaceX is constructed such that the Banach algebraL(X) of all continuous endomorphisms ofX admits a continuous homomorphism onto the Banach algebraC(βN) of all scalar valued functions on the Stone-Čech compacification of the positive integers with supremum norm. In particular:
(i) the cardinality of the set of all linear multiplicative functionals onL(X) is equal to 2c and (ii)X is not isomorphic to any finite Cartesian power of any Banach space. 相似文献
9.
If a separable Banach spaceX admits a real valued function ф with bounded nonempty support, φ 艂 is locally Lipschitzian and if no subspace ofX is isomorphic toc
o, thenX admits an equivalent twice Gateaux differentiable norm whose first Frechet differential is Lipschitzian on the unit sphere
ofX.
This author's research supported in part by NSERC (Canada) Grant A7535. 相似文献
10.
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
11.
M. Valdivia 《Israel Journal of Mathematics》1990,71(3):289-296
LetY andZ be two closed subspaces of a Banach spaceX such thatY≠lcub;0rcub; andY+Z=X. Then, ifZ is weakly countably determined, there exists a continuous projectionT inX such that ∥T∥=1,T(X)⊃Y, T
−1(0)⊂Z and densT(X)=densY. It follows that every Banach spaceX is the topological direct sum of two subspacesX
1 andX
2 such thatX
1 is reflexive and densX
2**=densX**/X. 相似文献
12.
An elementary proof of the (known) fact that each element of the Banach spaceℓ
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 ofℓ
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
13.
Libor Veselý 《Archiv der Mathematik》2002,79(6):499-506
Given a Banach spaceX, letc
0(X) be the space of all null sequences inX (equipped with the supremum norm). We show that: 1) each compact set inc
0(X) admits a (Chebyshev) center iff each compact set inX admits a center; 2) forX satisfying a certain condition (Q), each bounded set inc
0(X) admits a center iffX is quasi uniformly rotund. We construct a Banach spaceX such that the compact subsets ofX admit centers,X satisfies the condition (Q) andX is not quasi uniformly rotund. It follows that the Banach spaceE=c
0(X) has the property from the title.
Eine überarbeitete Fassung ging am 4. 7. 2001 ein 相似文献
14.
M. Edelstein 《Israel Journal of Mathematics》1969,7(1):90-94
LetA be a finite nonempty family of nonempty disjoint closed and bounded sets in a Banach spaceE which is either separable and the conjugate of some Banach spaceX (i.e.E=X*) or, reflexive and locally uniformly convex. IfC denotes the weak*-closed convex hull of ∪ {A:A ∈A} then the set of points inE ∼C through which there is no hyperplane intersecting exactly one member ofA is discrete (or empty).
This research was supported by the National Research Council of Canada, Grant A-3999. 相似文献
15.
T. S. S. R. K. Rao 《Proceedings Mathematical Sciences》1999,109(1):75-85
For 1 ≤p ≤ ∞ we show that there are no denting points in the unit ball of ℓ(lp). This extends a result recently proved by Grząślewicz and Scherwentke whenp = 2 [GS1]. We also show that for any Banach spaceX and for any measure space (Ω, A, μ), the unit ball of ℓ(L
1 (μ), X) has denting points iffL
1(μ) is finite dimensional and the unit ball ofX has a denting point. We also exhibit other classes of Banach spacesX andY for which the unit ball of ℓ(X, Y) has no denting points. When X* has the extreme point intersection property, we show that all ‘nice’ operators in the unit
ball of ℓ(X, Y) are strongly extreme points. 相似文献
16.
K. Jarosz 《Israel Journal of Mathematics》1988,64(1):49-56
For any Banach spaceX there is a norm |||·||| onX, equivalent to the original one, such that (X, |||·|||) has only trivial isometries. For any groupG there is a Banach spaceX such that the group of isometries ofX is isomorphic toG × {− 1, 1}. For any countable groupG there is a norm ‖ · ‖
G
onC([0, 1]) equivalent to the original one such that the group of isometries of (C([0, 1]), ‖ · ‖
G
) is isomorphic toG × {−1, + 1}. 相似文献
17.
The invariant subspace problem for a class of Banach spaces, 2: Hypercyclic operators 总被引:2,自引:0,他引:2
C. J. Read 《Israel Journal of Mathematics》1988,63(1):1-40
We continue here the line of investigation begun in [7], where we showed that on every Banach spaceX=l
1⊗W (whereW is separable) there is an operatorT with no nontrivial invariant subspaces. Here, we work on the same class of Banach spaces, and produce operators which not
only have no invariant subspaces, but are also hypercyclic. This means that for every nonzero vectorx inX, the translatesT
r x (r=1, 2, 3,...) are dense inX. This is an interesting result even if stated in a form which disregards the linearity ofT: it tells us that there is a continuous map ofX{0\{ into itself such that the orbit {T
rx :r≧0{ of anyx teX \{0\{ is dense inX \{0\{. The methods used to construct the new operatorT are similar to those in [7], but we need to have somewhat greater complexity in order to obtain a hypercyclic operator. 相似文献
18.
We show that for a separable Banach spaceX failing the Radon-Nikodym property (RNP), andε > 0, there is a symmetric closed convex subsetC of the unit ball ofX such that every extreme point of the weak-star closure ofC in the bidualX** has distance fromX bigger than 1 −ε. An example is given showing that the full strength of this theorem does not carry over to the non-separable case. However,
admitting a renorming, we get an analogous result for this theorem in the non-separable case too. We also show that in a Banach
space failing RNP there is, forε > 0, a convex setC of diameter equal to 1 such that each slice ofC has diameter bigger than 1 −ε. Some more related results about the geometry of Banach spaces failing RNP are given. 相似文献
19.
A closed, convex and bounded setP in a Banach spaceE is called a polytope if every finite-dimensional section ofP is a polytope. A Banach spaceE is called polyhedral ifE has an equivalent norm such that its unit ball is a polytope. We prove here:
We deduce from these two results that in a polyhedral Banach space (for instance in c0(ℕ) or inC(K) forK countable compact), every equivalent norm can be approximated by norms which are analytic onE/{0}. 相似文献
(1) | LetW be an arbitrary closed, convex and bounded body in a separable polyhedral Banach spaceE and let ε>0. Then there exists a tangential ε-approximating polytopeP for the bodyW. |
(2) | LetP be a polytope in a separable Banach spaceE. Then, for every ε>0,P can be ε-approximated by an analytic, closed, convex and bounded bodyV. |
20.
A. Szankowski 《Israel Journal of Mathematics》1972,11(3):292-296
We construct a separable reflexive Banach spaceX which is complementably universal for all finite dimensional Banach spaces. By this we mean: for every finite dimensional
Banach spaceE there is isometric embeddingi:E→X such that there exists a projectionP: →
→
onto
with ‖P‖=1. 相似文献