共查询到20条相似文献,搜索用时 15 毫秒
1.
It is shown that for every separable Banach space X with non-separable dual, the space contains an unconditional family of size . The proof is based on Ramsey Theory for trees and finite products of perfect sets of reals. Among its consequences, it
is proved that every dual Banach space has a separable quotient. 相似文献
2.
Jerzy Ka?kol Wies?aw ?liwa 《Topology and its Applications》2011,158(9):1131-1135
It is known that within metric spaces analyticity and K-analyticity are equivalent concepts. It is known also that non-separable weakly compactly generated (shortly WCG) Banach spaces over R or C provide concrete examples of weakly K-analytic spaces which are not weakly analytic. We study the case which totally differs from the above one. A general theorem is provided which shows that a Banach space E over a locally compact non-archimedean non-trivially valued field is weakly Lindelöf iff E is separable iff E is WCG iff E is weakly web-compact (in the sense of Orihuela). This provides a non-archimedean version of a remarkable Amir-Lindenstrauss theorem. 相似文献
3.
Valentin Ferenczi 《Advances in Mathematics》2005,195(1):259-282
We show that any Banach space contains a continuum of non-isomorphic subspaces or a minimal subspace. We define an ergodic Banach space X as a space such that E0 Borel reduces to isomorphism on the set of subspaces of X, and show that every Banach space is either ergodic or contains a subspace with an unconditional basis which is complementably universal for the family of its block-subspaces. We also use our methods to get uniformity results. We show that an unconditional basis of a Banach space, of which every block-subspace is complemented, must be asymptotically c0 or ?p, and we deduce some new characterisations of the classical spaces c0 and ?p. 相似文献
4.
Spiros A. Argyros 《Advances in Mathematics》2007,209(2):666-748
We study universality problems in Banach space theory. We show that if A is an analytic class, in the Effros-Borel structure of subspaces of C([0,1]), of non-universal separable Banach spaces, then there exists a non-universal separable Banach space Y, with a Schauder basis, that contains isomorphs of each member of A with the bounded approximation property. The proof is based on the amalgamation technique of a class C of separable Banach spaces, introduced in the paper. We show, among others, that there exists a separable Banach space R not containing L1(0,1) such that the indices β and rND are unbounded on the set of Baire-1 elements of the ball of the double dual R∗∗ of R. This answers two questions of H.P. Rosenthal.We also introduce the concept of a strongly bounded class of separable Banach spaces. A class C of separable Banach spaces is strongly bounded if for every analytic subset A of C there exists Y∈C that contains all members of A up to isomorphism. We show that several natural classes of separable Banach spaces are strongly bounded, among them the class of non-universal spaces with a Schauder basis, the class of reflexive spaces with a Schauder basis, the class of spaces with a shrinking Schauder basis and the class of spaces with Schauder basis not containing a minimal Banach space X. 相似文献
5.
A Banach space is hereditarily finitely decomposable if it does not
contain finite direct sums of infinite dimensional subspaces with
arbitrarily large number of summands. Here we show that the class of all
hereditarily finitely decomposable Banach spaces has the three-space
property. Moreover we show that the corresponding class defined in terms
of quotients has also the three-space property. 相似文献
6.
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
7.
We construct a family (Xγ) of reflexive Banach spaces with long (countable as well as uncountable) transfinite bases but with no unconditional basic sequences. The method we introduce to achieve this allows us to considerably control the structure of subspaces of the resulting spaces as well as to precisely describe the corresponding spaces on non-strictly singular operators. For example, for every pair of countable ordinals γ,β, we are able to decompose every bounded linear operator from Xγ to Xβ as the sum of a diagonal operator and an strictly singular operator. We also show that every finite-dimensional subspace of any member Xγ of our class can be moved by and (4+?)-isomorphism to essentially any region of any other member Xδ or our class. Finally, we find subspaces X of Xγ such that the operator space L(X,Xγ) is quite rich but any bounded operator T from X into X is a strictly singular pertubation of a scalar multiple of the identity. 相似文献
8.
J.L. Ansorena 《Quaestiones Mathematicae》2018,41(5):615-628
We revisit the concept of a subsymmetric norm and construct a subsymmetric renorming of a Banach space with a subsymmetric basis. As a by-product of our work we introduce the concept of a lower symmetric basis and investigate its connection with subsymmetric bases and subsymmetric renormings. 相似文献
9.
Banach spaces with small spaces of operators 总被引:16,自引:0,他引:16
10.
We prove that a WLD subspace of the space consisting of all bounded, countably supported functions on a set Γ embeds isomorphically into if and only if it does not contain isometric copies of . Moreover, a subspace of is constructed that has an unconditional basis, does not embed into , and whose every weakly compact subset is separable (in particular, it cannot contain any isomorphic copies of ). 相似文献
11.
12.
Relatively recently it was proved that if Γ is an arbitrary set, then any equivalent norm on can be approximated uniformly on bounded sets by polyhedral norms and smooth norms, with arbitrary precision. We extend this result to more classes of spaces having uncountable symmetric bases, such as preduals of the ‘discrete’ Lorentz spaces , and certain symmetric Nakano spaces and Orlicz spaces. We also show that, given an arbitrary ordinal number α, there exists a scattered compact space K having Cantor–Bendixson height at least α, such that every equivalent norm on can be approximated as above. 相似文献
13.
Valentin Ferenczi 《Advances in Mathematics》2007,213(1):462-488
There exists a real hereditarily indecomposable Banach space X=X(C) (respectively X=X(H)) such that the algebra L(X)/S(X) is isomorphic to C (respectively to the quaternionic division algebra H).Up to isomorphism, X(C) has exactly two complex structures, which are conjugate, totally incomparable, and both hereditarily indecomposable. So there exist two Banach spaces which are isometric as real spaces but totally incomparable as complex spaces. This extends results of J. Bourgain and S. Szarek [J. Bourgain, Real isomorphic complex Banach spaces need not be complex isomorphic, Proc. Amer. Math. Soc. 96 (2) (1986) 221-226; S. Szarek, On the existence and uniqueness of complex structure and spaces with “few” operators, Trans. Amer. Math. Soc. 293 (1) (1986) 339-353; S. Szarek, A superreflexive Banach space which does not admit complex structure, Proc. Amer. Math. Soc. 97 (3) (1986) 437-444], and proves that a theorem of G. Godefroy and N.J. Kalton [G. Godefroy, N.J. Kalton, Lipschitz-free Banach spaces, Studia Math. 159 (1) (2003) 121-141] about isometric embeddings of separable real Banach spaces does not extend to the complex case.The quaternionic example X(H), on the other hand, has unique complex structure up to isomorphism; other examples with a unique complex structure are produced, including a space with an unconditional basis and non-isomorphic to l2. This answers a question of S. Szarek in [S. Szarek, A superreflexive Banach space which does not admit complex structure, Proc. Amer. Math. Soc. 97 (3) (1986) 437-444]. 相似文献
14.
Jesús M.F. Castillo Manuel González Pier Luigi Papini 《Nonlinear Analysis: Theory, Methods & Applications》2012
We study the stability properties of the class of weak*-extensible spaces introduced by Wang, Zhao, and Qiang showing, among other things, that weak*-extensibility is equivalent to having a weak*-sequentially continuous dual ball (in short, w*SC) for duals of separable spaces or twisted sums of w*SC spaces. This shows that weak*-extensibility is not a 3-space property, solving a question posed by Wang, Zhao, and Qiang. We also introduce a restricted form of weak*-extensibility, called separable weak*-extensibility, and show that separably weak*-extensible Banach spaces have the Gelfand–Phillips property, although they are not necessarily w*SC spaces. 相似文献
15.
Jarno Talponen 《Topology and its Applications》2009,156(5):915-925
We will introduce the countable separation property (CSP) of Banach spaces X, which is defined as follows: X has CSP if each family E of closed linear subspaces of X whose intersection is the zero space contains a countable subfamily E0 with the same intersection. All separable Banach spaces have CSP and plenty of examples of non-separable CSP spaces are provided. Connections of CSP with Marku?evi?-bases, Corson property and related geometric issues are discussed. 相似文献
16.
The paper deals with the problem of the existence multi-orthogonal bases in finite-dimensional normed spaces over K, where K is a non-Archimedean complete valued field. 相似文献
17.
Albert Kubzdela 《Indagationes Mathematicae》2005,16(2):225-235
For linear subspaces of finite-dimensional normed spaces over K, where K is a non-Archimedean complete valued field which is not spherically complete, we study orthocomplementation as related to strictness and the Hahn-Banach property. We prove that there exist finite-dimensional normed spaces which possess non-orthocomplemented, strict HB-subspaces. 相似文献
18.
Petr Hájek 《Journal of Differential Equations》2010,249(12):3342-3351
We show that if X is an infinite-dimensional separable Banach space (or more generally a Banach space with an infinite-dimensional separable quotient) then there is a continuous mapping f:X→X such that the autonomous differential equation x′=f(x) has no solution at any point. 相似文献
19.
In this paper we use the Nash-Williams theory of fronts and barriers to study weakly null sequences in Banach spaces. Specifically, we show how barriers relate to the classical fact that C(K) with K a countable compactum is c0-saturated. Another result relates the notion of a barrier to the Maurey-Rosenthal example of a weakly null sequence with no unconditional subsequences. In particular, we construct examples of weakly-null sequences which are α-unconditional but not β-unconditional. 相似文献
20.
Assume that X, Y are real Banach spaces, Y has uniform convexity of type p (≥ 1), and f: X → Y is a standard coarse isometry. In this paper, we show that if
then there is a linear isometry U : X → Y so that
where is defined by
Representation properties of coarse isometries in free ultrafilter limits on are also discussed. 相似文献