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1.
We prove that each non-reflexive subspace ofJ * contains a subspace isomorphic toJ * and complmented inJ *. Consequences are thatJ is not isomorphic to any subspace ofJ *, and that every reflexive subspace ofJ is contained in a complemented reflexive subspace ofJ.  相似文献   

2.
《Quaestiones Mathematicae》2013,36(2):231-248
Abstract

The classical theorem of Dunford and Pettis identifies the bounded, uniformly integrable subsets of L1(μ) with the relatively weakly compact sets. Another characterization of uniform integrability is given in a theorem of De La Vallée Poussin which states that a subset K of L1 (μ) is bounded and uniformly integrable if and only if there is an N-function F so that sup{f F(f)dμ: f ε K} < ∞. De La Vallée Poussin's theorem is the focal point of the fmt part of this paper as well as the driving force for the results in the second part. We refine and improve this theorem in several directions. The theorem of De La Vallée Poussin does not, for instance, specify just how well the function F can be chosen. It gives little additional information in case the set in question is relatively norm compact in L1 (μ). Finally it gives no information on the structure of the set in the corresponding Band space of F-integrable functions. More specifically we establish the fact that a subset K of L1 is relatively compact if and only if there is an N-function F ε δ' so that K is relatively compact in L*F. Furthermore we prove that a subset K of L1 is relatively weakly compact if and only if there is an N-function F ε δ' so that K is relatively weakly compact in L*F. We then go on to show that a large class of non-reflexive Orlicz spaces has the weak Band-Saks property, by establishing a result for these spaces, very similar to the Dunford-Pettis theorem for L1.  相似文献   

3.
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   

4.
Let 1<α≦β<∞ andF be an arbitrary closed subset of the interval [α,β]. An Orlicz sequence spacel φ (resp. an Orlicz function spaceL φ(μ)) with associated indices α and β is found in such a way that the set of valuesp for which thel p-space is isomorphic to a complemented subspace ofl φ (resp.L φ(μ)) is precisely the given setF (resp.F ∪ {2}). Also, a recent result of Hernández and Peirats [1] is extended showing that, even for the case in which the indices satisfy αφ <2<βφ , there exist minimal Orlicz function spacesL φ(μ) with no complemented copy ofl p for anyp ≠ 2. Supported in part by CAICYT grant 0338-84.  相似文献   

5.
A typical result of the paper isTheorem. LetE be a reflexive subspace ofL 1 (Ω, A, P) [(Ω,A, P) a probability space]. IfE contains a subspace isomorphic to lp then for every ε > 0,E contains a subspace (1 + ε) isomorphic to lp. The technics are probability theory and ultraproducts.  相似文献   

6.
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 L1 space contained in a separable, conjugate space is isomorphic to a subspace of l1.  相似文献   

7.
Let 2<p<∞. The Banach space spanned by a sequence of independent random variables inL p , each of mean zero, is shown to be isomorphic tol 2,l p ,l 2l p , or a new spaceX p , and the linear topological properties ofX p are investigated. It is proved thatX p is isomorphic to a complemented subspace ofL p and another uncomplemented subspace ofL p , whence there exists an uncomplemented subspace ofl p isomorphic tol p . It is also proved thatX p is not isomorphic to the previously known p spaces. The work for this research was partially supported by the National Science Foundation GP-12997.  相似文献   

8.
It is shown that for every non-reflexive Banach spaceX withX **/X reflexive there exists a uniformly bounded sequence of projections {P n } n=1 whose ranges are uniformly isomorphic to {l p n } n = 1 either forp=1, orp=2 or forp=∞. The proof uses knowledge of the transfinite dualX ω, ESA Schauder decompositions and proof of a similar statement for spaces with an unconditional basis due to Tzafriri.  相似文献   

9.
We study reflexivity of bilattices. Some examples of reflexive and non-reflexive bilattices are given. With a given subspace lattice ? we may associate a bilattice Σ?. Similarly, having a bilattice Σ we may construct a subspace lattice Σ?. Connections between reflexivity of subspace lattices and associated bilattices are investigated. It is also shown that the direct sum of any two bilattices is never reflexive.  相似文献   

10.
Let E be the infinite-dimensional Grassmann algebra over a field F of characteristic zero, and consider L the F-vector space spanned by all generators of E. Let ? l be any fixed automorphism of E of order 2 such that L is an homogeneous subspace.

Our goal is to finish the computation of the sequences of ? l -codimensions, by finding its exact value for the unique open case, that is, when the subspace of L corresponding to the eigenvalue 1 is finite-dimensional. As a consequence we get the ?-codimensions for a large amount of arbitrary automorphisms ? of E of order 2.  相似文献   

11.
On the complemented subspaces problem   总被引:11,自引:0,他引:11  
A Banach space is isomorphic to a Hilbert space provided every closed subspace is complemented. A conditionally σ-complete Banach lattice is isomorphic to anL p -space (1≤p<∞) or toc 0(Γ) if every closed sublattice is complemented.  相似文献   

12.
Let Y be a reflexive subspace of the Banach space X, let (Ω, Σ, μ) be a finite measure space, and let L(μ, X) be the Banach space of all essentially bounded μ ‐Bochner integrable functions on Ω with values in X, endowed with its usual norm. Let us suppose that Σ0 is a sub‐σ ‐algebra of Σ, and let μ0 be the restriction of μ to Σ0. Given a natural number n, let N be a monotonous norm in ?n . We prove that L(μ, Y) is N ‐simultaneously proximinal in L(μ,X), and that if X is reflexive then L(μ0, X) is N ‐simultaneously proximinal in L(μ, X) in the sense of Fathi, Hussein, and Khalil [3]. (© 2008 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)  相似文献   

13.
We define the notion of “stable Banach space” by a simple condition on the norm. We prove that ifE is a stable Banach space, then every subspace ofL p(E) (1≦p<∞) is stable. Our main result asserts that every infinite dimensional stable Banach space containsl p, for somep, 1≦p<∞. This is a generalization of a theorem due to D. Aldous: every infinite dimensional subspace ofL 1 containsl p, for somep in the interval [1, 2].  相似文献   

14.
Inperpolation theory is used to develop a general pattern for proving the extension theorems mentioned in the title. In the case where the range space G is a w *-closed subspace of L or H with reflexive annihilator F, a necessary and sufficient condition on G is found for such an extension to always be possible. Specifically, F must be Hilbertian and become complemented in L p (1 < p 2) after a suitable change of density. Bibliography: 17 titles.  相似文献   

15.
Let ${\mathcal L}Let L{\mathcal L} be a subspace lattice on a Banach space X and suppose that ú{L ? L: L- < X}=X{\vee\{L\in\mathcal L: L_- < X\}=X} or ${\land\{L_- : L \in \mathcal L, L>(0)\}=(0)}${\land\{L_- : L \in \mathcal L, L>(0)\}=(0)} . Then each Jordan derivation from AlgL{\mathcal L} into B(X) is a derivation. This result can apply to completely distributive subspace lattice algebras, J{\mathcal J} -subspace lattice algebras and reflexive algebras with the non-trivial largest or smallest invariant subspace.  相似文献   

16.
Criteria for Orlicz spaces containing an isomorphic as well as an almost isometric complemented copy of l1 are given. The same is made for copies of l and c0 in Orlicz spaces and in the subspace of order continuous elements in Orlicz space, respectively. The Hahn-Banach theorem is not used in the constructions of the projections.  相似文献   

17.
We prove that a weakly compact operator fromH or any of its even duals into an arbitrary Banach space is uniformly convexifying. By using this, we establish three dicothomies: (1) every operator defined onH or any of its even duals either fixes a copy ofl or factors through a Banach space having the Banach-Saks property; (2) every quotient ofH or any of its even duals either contains a copy ofl or is super-reflexive; (3) every subspace ofL 1/H 0 1 or any of its even duals either contains a complemented copy ofl 1 or is super-reflexive.  相似文献   

18.
Let k and n be positive integers such that kn. Let Sn (F) denote the space of all n×n symmetric matrices over the field F with char F≠2. A subspace L of Sn (F) is said to be a k-subspace if rank Ak for every A?L.

Now suppose that k is even, and write k=2r. We say a k∥-subspace of Sn (F) is decomposable if there exists in Fn a subspace W of dimension n?r such that xtAx=0 for every x?W A?L.

We show here, under some mild assumptions on k n and F, that every k∥-subspace of Sn (F) of sufficiently large dimension must be decomposable. This is an analogue of a result obtained by Atkinson and Lloyd for corresponding subspaces of Fm,n .  相似文献   

19.
Lattice-universal Orlicz function spacesL F α,β[0, 1] with prefixed Boyd indices are constructed. Namely, given 0<α<β<∞ arbitrary there exists Orlicz function spacesL F α,β[0, 1] with indices α and β such that every Orlicz function spaceL G [0, 1] with indices between α and β is lattice-isomorphic to a sublattice ofL F α,β[0, 1]. The existence of classes of universal Orlicz spacesl Fα,β(I) with uncountable symmetric basis and prefixed indices α and β is also proved in the uncountable discrete case. Partially supported by BFM2001-1284.  相似文献   

20.
We discuss the computation of the secondary characteristic classes and of the holonomy classes for the leaves of locally homogeneous subfoliations. Furthermore, we shall construct some examples of locally homogeneous subfoliations (F 1, F 2) so that a leaf (L 1, L 2) of (F 1, F 2) admits non-trivial secondary characteristic classes and non-trivial holonomy classes which cannot be obtained if we consider each leaf separately.  相似文献   

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