共查询到20条相似文献,搜索用时 118 毫秒
1.
Valentin Ferenczi 《Journal of Functional Analysis》2009,257(1):149-1060
We prove three new dichotomies for Banach spaces à la W.T. Gowers' dichotomies. The three dichotomies characterise respectively the spaces having no minimal subspaces, having no subsequentially minimal basic sequences, and having no subspaces crudely finitely representable in all of their subspaces. We subsequently use these results to make progress on Gowers' program of classifying Banach spaces by finding characteristic spaces present in every space. Also, the results are used to embed any partial order of size ℵ1 into the subspaces of any space without a minimal subspace ordered by isomorphic embeddability. 相似文献
2.
《Bulletin des Sciences Mathématiques》2007,131(3):291-324
As far as we know, the exterior product with any norm has not been studied for Banach spaces. Especially, no studies have been done on Grassmann manifolds in Banach spaces. We think it is important to study these because simple m-vectors can be thought of as m-dimensional subspaces scaled in some way according to our work. We hope Banach space norms of simple m-vectors will yield metric information about their associated subspaces. In fact, this is the case with m-uniform convexity and m-uniform rotundity which are associated with area (in Banach spaces). 相似文献
3.
《Comptes Rendus de l'Academie des Sciences Series IIA Earth and Planetary Science》2001,332(2):151-156
We show that the consideration of Gâteaux smooth functions on Banach spaces which admit an equivalent Gâteaux smooth norm allows us to show that certain linear operators have nontrivial closed invariant subspaces. It is in particular the case of all operators on a real Banach space which admit a moment sequence. 相似文献
4.
M. Raja 《Israel Journal of Mathematics》2002,129(1):77-91
We show that the existence of an equivalent dual LUR norm on a dual Banach space can be characterized by a topological property
similar to the fragmentability. The compact spaces homeomorphic to weak* compact subsets of a dual LUR Banach space have the
same properties as the class of Radon-Nikodym compact spaces.
Research supported by the DGICYT PB 95-1025. 相似文献
5.
We characterize the minimal and maximal operator ideals associated, in the sense of Defant and Floret, to a wide class of tensor norms derived from a Banach sequence space. Our results are extensions of classical ones about tensor norms of Saphar [Studia Math. 38 (1972) 71-100] and show the key role played by the structure of finite-dimensional subspaces in this kind of problems. 相似文献
6.
On Some Applications of Geometry of Banach Spaces and Some New Results Related to the Fixed Point Theory in Orlicz Sequence Spaces 下载免费PDF全文
Yunan Cui Henryk Hudzik Radosław Kaczmarek Haifeng Ma Yuwen Wang & Meiling Zhang 《数学研究》2016,49(4):325-378
We present some applications of the geometry of Banach spaces in the approximation
theory and in the theory of generalized inverses. We also give some new
results, on Orlicz sequence spaces, related to the fixed point theory. After a short introduction, in Section 2 we
consider the best approximation projection from a Banach space $X$ onto its non-empty
subset and proximinality of the subspaces of order continuous elements in various
classes of Köthe spaces. We present formulas for the distance to these subspaces of
the elements from the outside of them. In Section 3 we recall some results and definitions
concerning generalized inverses of operators (metric generalized inverses and
Moore-Penrose generalized inverses). We also recall some results on the perturbation
analysis of generalized inverses in Banach spaces. The last part of this section concerns
generalized inverses of multivalued linear operators (their definitions and representations).
The last section starts with a formula for modulus of nearly uniform
smoothness of Orlicz sequence spaces $\ell^\Phi$equipped with the Amemiya-Orlicz norm.
From this result a criterion for nearly uniform smoothness of these spaces is deduced.
A formula for the Domínguez-Benavides coefficient $R(a,l_\Phi)$ is also presented, whence
a sufficient condition for the weak fixed point property of the space $\ell^\Phi$is obtained. 相似文献
7.
In this note we study the problem how the complexification of a real Banach space can be normed in such a way that it becomes a complex Banach space from the point of view of the theory of cross-norms on tensor products of Banach spaces. In particular we show that the norm of a complex Banach lattice can be interpretated in terms of the l-tensor product of real Banach lattices. 相似文献
8.
IfX is a Banach space such thatX, X* are subspaces of Banach spaces generated by weakly-compact sets, thenX is also generated by a weakly-compact set and admits an equivalent Fréchet smooth norm. 相似文献
9.
S. Simons 《Set-Valued and Variational Analysis》2014,22(1):259-270
This paper is about certain linear subspaces of Banach SN spaces (that is to say Banach spaces which have a symmetric nonexpansive linear map into their dual spaces). We apply our results to monotone linear subspaces of the product of a Banach space and its dual. In this paper, we establish several new results and also give improved proofs of some known ones in both the general and the special contexts. 相似文献
10.
V. D. Stepanov 《Mathematical Notes》2015,98(5-6):957-970
Optimal (minimal) Banach spaces containing given cones of monotone or quasiconcave functions on the semiaxis from weighted Lebesgue spaces are described. Exact formulas for the norm of the optimal space are presented. All cases of the summation parameter are studied. 相似文献
11.
We characterize norm hermitian operators on classes of tensor products of Banach spaces and derive results for the particular
settings of injective and projective tensor products. We provide a characterization of bi-circular and generalized bi-circular
projections on tensor products of Banach spaces supporting only dyadic surjective isometries.
Received: 26 February 2007, Revised: 30 May 2007 相似文献
12.
R. M. Causey 《Positivity》2018,22(5):1197-1221
We provide a short characterization of p-asymptotic uniform smoothability and asymptotic uniform flatenability of operators and of Banach spaces. We use these characterizations to show that many asymptotic uniform smoothness properties pass to injective tensor products of operators and of Banach spaces. In particular, we prove that the injective tensor product of two asymptotically uniformly smooth Banach spaces is asymptotically uniformly smooth. We prove that for \(1<p<\infty \), the class of p-asymptotically uniformly smoothable operators can be endowed with an ideal norm making this class a Banach ideal. We also prove that the class of asymptotically uniformly flattenable operators can be endowed with an ideal norm making this class a Banach ideal. 相似文献
13.
M. I. Ostrovskii 《Proceedings of the American Mathematical Society》1996,124(7):2005-2012
It is proved that there exist complemented subspaces of countable topological products (locally convex direct sums) of Banach spaces which cannot be represented as topological products (locally convex direct sums) of Banach spaces.
14.
Vladimir G. Troitsky 《Proceedings of the American Mathematical Society》2004,132(4):1177-1180
We extend the method of minimal vectors to arbitrary Banach spaces. It is proved, by a variant of the method, that certain quasinilpotent operators on arbitrary Banach spaces have hyperinvariant subspaces.
15.
Sh. Rezapour 《分析论及其应用》2003,19(2):130-135
We will define and characterize ε-weakly Chebyshev subspaces of Banach spaces. We will prove that all closed subspaces of
a Banach space X are ε-weakly Chebyshev if and only if X is reflexive. 相似文献
16.
José Bonet Félix Martínez-Giménez 《Journal of Mathematical Analysis and Applications》2004,297(2):599-611
We use tensor product techniques to study universality, hypercyclicity and chaos of multipliers defined on operator ideals and of multiplication operators on the space of all continuous and linear operators, thus continuing the work of Kit Chan. We also obtain the first examples of outer multipliers on a Banach algebra which are chaotic in the sense of Devaney, and prove sufficient conditions for the existence of closed subspaces of universal vectors for operators between Fréchet spaces. 相似文献
17.
Sh. Rezapour 《分析论及其应用》2003,19(2):130-135
We will define and characterize ε-weakly Chebyshev subspaces of Banach spaces. We will prove that all closed subspaces of
a Banach space X are ε-weakly Chebyshev if and only if X is reflexive. 相似文献
18.
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
19.
M. Fabian G. Godefroy V. Zizler 《Journal of Mathematical Analysis and Applications》2004,297(2):419-455
We give characterizations of weakly compactly generated spaces, their subspaces, Vašák spaces, weakly Lindelöf determined spaces as well as several other classes of Banach spaces related to uniform Gâteaux smoothness, in terms of the presence of a total subset of the space with some additional properties. In addition, we describe geometrically, when possible, these classes by means of suitable smoothness or rotundity of the norm. As a consequence, we get new, functional analytic proofs of several theorems on (uniform) Eberlein, Gul'ko and Talagrand compacta. 相似文献
20.
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