共查询到20条相似文献，搜索用时 15 毫秒
1.
On Hereditarily Indecomposable Banach Spaces 总被引：1，自引：0，他引：1
Li Xin CHENG Huai Jie ZHONG 《数学学报(英文版)》2006,22(3):751-756
This paper shows that every non-separable hereditarily indecomposable Banach space admits an equivalent strictly convex norm, but its bi-dual can never have such a one; consequently, every non-separable hereditarily indecomposable Banach space has no equivalent locally uniformly convex norm. 相似文献
2.
Spiros A. Argyros 《Proceedings of the American Mathematical Society》2001,129(11):3231-3239
It is shown that every separable Banach space universal for the class of reflexive Hereditarily Indecomposable space contains isomorphically and hence it is universal for all separable spaces. This result shows the large variety of reflexive H.I. spaces.
3.
N. Ottavy 《Journal of Optimization Theory and Applications》1988,56(3):433-461
Many mathematical and applied problems can be reduced to finding a common point of a system of convex sets. The aim of this paper is twofold: first, to present a unified framework for the study of all the projection-like methods, both parallel and serial (chaotic, mostremote set, cyclic order, barycentric, extrapolated, etc.); second, to establish strong convergence results for quite general sets of constraints (generalized Slater, generalized uniformly convex, made of affine varieties, complementary, etc.). This is done by introducing the concept of regular family. We proceed as follows: first, we present definitions, assumptions, theorems, and conclusions; thereafter, we prove them. 相似文献
4.
We extend the Gustavsson–Peetre method to the context of N ‐tuples of Banach spaces. We give estimates for the norm of the interpolated operator. The method is applied to tuples of weighted L p ‐spaces and to tuples of Orlicz spaces identifying the outcoming spaces in both cases. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
5.
A. Manoussakis 《Proceedings of the American Mathematical Society》2003,131(8):2515-2525
We prove that if a Banach space with a bimonotone shrinking basis does not contain spreading models but every block sequence of the basis contains a further block sequence which is a spreading model for every , then every subspace has a further subspace which is arbitrarily distortable. We also prove that a mixed Tsirelson space , such that , does not contain spreading models.
6.
Piotr Minc 《Transactions of the American Mathematical Society》2000,352(2):643-654
A hereditarily indecomposable tree-like continuum without the fixed point property is constructed. The example answers a question of Knaster and Bellamy.
7.
8.
We prove in this paper that the Hilbert geometry associated with a bounded open convex domain
in R
n
whose boundary
is a
2 hypersuface with nonvanishing Gaussian curvature is bi-Lipschitz equivalent to the n-dimensional hyperbolic space H
n
. Moreover, we show that the balls in such a Hilbert geometry have the same volume growth entropy as those in H
n
. 相似文献
9.
Michael Levin 《Proceedings of the American Mathematical Society》1997,125(2):603-609
We prove the following theorems:
Theorem 1. Let be an -dimensional hereditarily indecomposable continuum. Then there exist -dimensional hereditarily indecomposable continua and monotone maps such that is an embedding and the space of all subcontinua of is embeddable in by .
Theorem 2. For every open monotone map with non-trivial sufficiently small fibers on a finite dimensional hereditarily indecomposable continuum with there exists a -dimensional subcontinuum such that and the restriction of to is also monotone and open.
The connection between these theorems and other results in Hyperspace theory is studied.
10.
Thomas E. Gonzalez 《Proceedings of the American Mathematical Society》2003,131(12):3925-3927
In 1947, W.H. Gottschalk proved that no dendrite is the continuous, exactly -to-1 image of any continuum if . Since that time, no other class of continua has been shown to have this same property. It is shown that no hereditarily indecomposable tree-like continuum is the continuous, exactly -to-1 image of any continuum if .
11.
Teresa Bermú dez Antonio Bonilla Antonio Martinó n 《Proceedings of the American Mathematical Society》2003,131(8):2435-2441
We prove that every separable infinite dimensional complex Banach space admits a hypercyclic uniformly continuous semigroup. We also prove that there exist Banach spaces admitting no chaotic strongly continuous semigroups.
12.
Güllü Canan Hazar Güle 《Mathematical Methods in the Applied Sciences》2019,42(16):5398-5402
By , we denote the set of all sequences such that Σ?nan is summable V whenever Σan is summable U, where U and V are two summability methods. Recently, Sar?göl has characterized the set for k > 1,α > ?1 and arbitrary positive sequences Now, in the present paper, we characterize the sets , k > 1 and , k ≥ 1 for arbitrary positive sequences Hence we extend these results to the range α≥ ? 1. In this way, some open problems in this topic are also completed. 相似文献
13.
Francis Jordan Sam B. Nadler Jr. 《Proceedings of the American Mathematical Society》2001,129(4):1219-1228
It is shown that a continuum that is an space in the sense of Michael must be hereditarily decomposable. This improves known results, thereby providing more evidence that such continua must be dendrites.
14.
Michael Levin Yaki Sternfeld 《Proceedings of the American Mathematical Society》1997,125(9):2771-2775
Let be a metric continuum and let denote the space of subcontinua of with the Hausdorff metric. We settle a longstanding problem showing that if then . The special structure and properties of hereditarily indecomposable continua are applied in the proof.
15.
Hüseyin Bor 《Proceedings Mathematical Sciences》1992,102(2):125-128
In this paper we have established a relation between |R,p
n
;δ|k and |R,q
n
;δ|k summability methods which generalizes the results of Bor [1] and Bosanquet [2]. 相似文献
16.
17.
In this paper we first discuss the relations between some G-M-type spaces, and the previous eight kinds of G-M-type Banach spaces are merged into four different kinds. Then we build a Generalized Operator Extension Theorem, and introduce the concept of complete minimal sequences. Some sufficient and necessary conditions under which a Banach space is a hereditarily indecomposable space are given. Finally, we give some characterizations of hereditarily indecomposable Banach Spaces. 相似文献
18.
We show that Ramsey theory, a domain presently conceived to guarantee the existence of large homogeneous sets for partitions on -tuples of words (for every natural number ) over a finite alphabet, can be extended to one for partitions on Schreier-type sets of words (of every countable ordinal). Indeed, we establish an extension of the partition theorem of Carlson about words and of the (more general) partition theorem of Furstenberg-Katznelson about combinatorial subspaces of the set of words (generated from -tuples of words for any fixed natural number ) into a partition theorem about combinatorial subspaces (generated from Schreier-type sets of words of order any fixed countable ordinal). Furthermore, as a result we obtain a strengthening of Carlson's infinitary Nash-Williams type (and Ellentuck type) partition theorem about infinite sequences of variable words into a theorem, in which an infinite sequence of variable words and a binary partition of all the finite sequences of words, one of whose components is, in addition, a tree, are assumed, concluding that all the Schreier-type finite reductions of an infinite reduction of the given sequence have a behavior determined by the Cantor-Bendixson ordinal index of the tree-component of the partition, falling in the tree-component above that index and in its complement below it.
19.
称局部凸空间（E,(?)0）为WCM空间若对于任何弱于(?)0的局部凸拓扑(?),（E,(?)）与（E,(?)0）具相同的弱紧圆凸集.本文研究了WCM空间的存在性及其与其他类型局部凸空间之间的关系,还给出了WCM空间的一种映照特征. 相似文献
20.
Jo W. Heath 《Proceedings of the American Mathematical Society》1996,124(11):3571-3578
Some thirteen years ago S. B. Nadler, Jr. and L. E. Ward, Jr., asked if any treelike continuum could be the 2-to-1 image of a continuum. In fact, it has been conjectured that the property of being treelike characterizes those continua that are not the 2-to-1 image of any continuum. But the characterization must be something else; this paper shows that many pseudo-solenoids are not the 2-to-1 image of any continuum.