共查询到20条相似文献,搜索用时 843 毫秒
1.
S. Lajara A.J. Pallars S. Troyanski 《Journal of Mathematical Analysis and Applications》2009,350(2):630-639
Given a separable Banach space X with no isomorphic copies of ℓ1 and a separable subspace Y of its bidual, we provide a sufficient condition on Y to ensure that X admits an equivalent norm such that the restriction to Y of the corresponding bidual norm is midpoint locally uniformly rotund. This result applies to the separable subspaces of the bidual of a Banach space with a shrinking unconditional Schauder basis and to the bidual of the James space. 相似文献
2.
Andrzej Szankowski 《Israel Journal of Mathematics》1973,15(1):53-59
Every reflexive Banach space with unconditional basis is isomorphic to a complemented subspace of a reflexive Banach space
with symmetric basis. 相似文献
3.
Joram Lindenstrauss 《Israel Journal of Mathematics》1972,13(3-4):317-320
Every separable Banach space with an unconditional basis is isomorphic to a complemented subspace of a space with a symmetric
basis. 相似文献
4.
Wolfgang Lusky 《Journal of Functional Analysis》1985,62(1):1-7
It is shown that every separable Banach space X containing a subspace isomorphic to c0 has a subspace Y with basis such that and the latter space has a shrinking basis and an unconditional FDD. Moreover, it is shown that X ⊕ C∞ has a basis if X has the bounded approximation property. 相似文献
5.
Henryk Hudzik Yuwen Wang Ruli Sha 《Numerical Functional Analysis & Optimization》2013,34(7-8):779-790
In this paper, we extend the Moreau (Riesz) decomposition theorem from Hilbert spaces to Banach spaces. Criteria for a closed subspace to be (strongly) orthogonally complemented in a Banach space are given. We prove that every closed subspace of a Banach space X with dim X ≥ 3 (dim X ≤ 2) is strongly orthognally complemented if and only if the Banach space X is isometric to a Hilbert space (resp. strictly convex), which is complementary to the well-known result saying that every closed subspace of a Banach space X is topologically complemented if and only if the Banach space X is isomorphic to a Hilbert space. 相似文献
6.
This paper first presents a characterization of three classes of negligible closed convex sets (i.e., Gauss null sets, Aronszajn null sets and cube null sets) in terms of non-support points; then gives a generalization of Gâteaux differentiability theorems of Lipschitz mapping from open sets to those closed convex sets admitting non-support points; and as their application, finally shows that a closed convex set in a separable Banach space X can be Lipschitz embedded into a Banach space Y with the Radon–Nikodym property if and only if the closure of its linear span is linearly isomorphic to a closed subspace of Y. 相似文献
7.
A Solution to Banach's Hyperplane Problem 总被引:4,自引:0,他引:4
An infinite-dimensional Banach space X is constructed whichis not isomorphic to X R. Equivalently, X is not isomorphicto any of its closed subspaces of codimension one. This givesa negative answer to a question of Banach. In fact, X has thestronger property that it is not isomorphic to any proper subspace.It also happens to have an unconditional basis. 相似文献
8.
E. Medina Galego 《Archiv der Mathematik》2002,79(4):299-307
We investigate the geometry of the Banach spaces failing Schroeder-Bernstein Property (SBP). Initially we prove that every complex hereditarily indecomposable Banach space H is isomorphic to a complemented subspace of a Banach space S(H) that fails SBP in such a way that the only complemented hereditarily indecomposable subspaces of S(H) are those which are nearly isomorphic to H. Then we show that every Banach space having Mazur property is isomorphic to some complemented subspace of a Banach space which is not isomorphic to its square but isomorphic to its cube. Finally, we prove that if a Banach space X fails SBP then either it is not primary or the Grothendieck group K0(L(X)) of the algebra of operators on X is not trivial. 相似文献
9.
We study the intersection operation of closed linear subspaces in a separable Banach space. We show that if the ambient space is quasi-reflexive, then the intersection operation is Borel. On the other hand, if the space contains a closed subspace with a Schauder decomposition into infinitely many non-reflexive spaces, then the intersection operation is not Borel. As a corollary, for a closed subspace of a Banach space with an unconditional basis, the intersection operation of the closed linear subspaces is Borel if and only if the space is reflexive. We also consider the intersection operation of additive subgroups in an infinite-dimensional separable Banach space, and show that if this intersection operation is Borel then the space is hereditarily indecomposable. 相似文献
10.
《数学学报(英文版)》2015,(5)
Norming subspaces are studied widely in the duality theory of Banach spaces. These subspaces are applied to the Borel and Baire classifications of the inverse operators. The main result of this article asserts that the dual of a Banach space X contains a norming subspace isomorphic to 1 provided that the following two conditions are satisfied:(1) X*contains a subspace isomorphic to 1;and(2) X*contains a separable norming subspace. 相似文献
11.
Ka-Sing Lau 《Journal of Approximation Theory》1977,21(4):319-327
A closed subspace F in a Banach space X is called almost Chebyshev if the set of x ε X which fail to have unique best approximation in F is contained in a first category subset. We prove, among other results, that if X is a separable Banach space which is either locally uniformly convex or has the Radon-Nikodym property, then “almost all” closed subspaces are almost Chebyshev. 相似文献
12.
In this paper, we introduce a new iterative procedure which is constructed by the shrinking hybrid projection method for solving the common solution of fixed point problems for two total quasi-?-asymptotically nonexpansive multi-valued mappings. Under suitable conditions, the strong convergence theorems are established in a uniformly smooth and strictly convex real Banach space with Kadec-Klee property. Our result improves and extends the corresponding ones announced by some authors. 相似文献
13.
A. Szankowski 《Israel Journal of Mathematics》1976,24(3-4):329-337
A Banach latticeL without the approximation property is constructed. The construction can be improved so thatL is, in addition, uniformly convex. These results yield the existence of a uniformly convex Banach space with symmetric basis
and without the uniform approximation property. 相似文献
14.
Rudolf Brigola 《manuscripta mathematica》1983,44(1-3):95-102
It is proved that a WCG Banach space X is isomorphic to a conjugate Banach space if and only if there exists a closed subspace V of its conjugate space X' with positive characteristic such that X possesses the following summability property with respect to V: For every bounded sequence in X there exists a regular essentially positive summability method A such that the A-means of the sequence are σ(X,V)-convergent in X. This extends a well-known theorem of Nishiura-Waterman [8] and yields an analogous characterization of quasi-reflexive spaces. Conjugate spaces of smooth Banach spaces can also be characterized by the above summability condition. 相似文献
15.
A. E. Tong 《Israel Journal of Mathematics》1971,10(4):451-456
It is proved that if the Banach spaceE has an unconditional basis and ifF is another Banach space, the following two assertions are equivalent: (1) There is a non-compact bounded linear operator
fromE intoF′. (2) The space of bounded linear operators fromE intoF′ has a subspace isomorphic toc
0.
This research was supported in part by National Science Foundation Grants GP 12027 and GU 3171.
The author thanks the referee for simplifying the proof. 相似文献
16.
William J. Davis 《Israel Journal of Mathematics》1975,20(2):189-191
Every super-reflexive space with an unconditional basis is isomorphic to a complemented subspace of a super-reflexive space with a symmetric basis. 相似文献
17.
Sofiya Ostrovska 《数学学报(英文版)》2015,31(5):767-771
Norming subspaces are studied widely in the duality theory of Banach spaces. These subspaces are applied to the Borel and Baire classifications of the inverse operators. The main result of this article asserts that the dual of a Banach space X contains a norming subspace isomorphic to l1 provided that the following two conditions are satisfied: (1) X* contains a subspace isomorphic to l1; and (2) X* contains a separable norming subspace. 相似文献
18.
Using the concept of asymptotic center we obtain the existence of fixed points having preassigned location for a wider class of asymptotic nonexpansive mappings in a uniformly convex Banach space. This generalization leads us to get a recent result of Alfuraidan and Khamsi for continuous monotone asymptotic nonexpansive mappings as well as the classical fixed-point result of Geobel and Kirk for asymptotic nonexpansive mappings in a uniformly convex Banach space. Also we prove a fixed-point theorem for order preserving continuous maps on a quasiordered closed convex subset of a uniformly convex Banach sapce having monotone norm. 相似文献
19.
Jesús Bastero 《Israel Journal of Mathematics》1986,53(3):373-380
In this paper we prove the following result which solves a question raised by A. Pelczynski: “Every stable Banach space with
an unconditional basis is isomorphic to a complemented subspace of some stable Banach space with a symmetric basis.” Moreover,
we show that all the interpolation spacesl
p
,l
q
θ,X,1 1≦p, q<∞ andX stable, are stable. 相似文献
20.
The main result of this paper is that a closed convex subset of a Banach space has the fixed point property for nonexpansive mappings if and only if it has the fixed point property for nonexpansive semigroups. 相似文献