نتایج جستجو برای: banach spaces

تعداد نتایج: 136556  

2014
Francis J. Narcowich

A sequence {vj} is said to be Cauchy if for each > 0, there exists a natural number N such that ‖vj−vk‖ < for all j, k ≥ N . Every convergent sequence is Cauchy, but there are many examples of normed linear spaces V for which there exists non-convergent Cauchy sequences. One such example is the set of rational numbers Q. The sequence (1.4, 1.41, 1.414, . . . ) converges to √ 2 which is not a ra...

2000
JOSÉ IOVINO

0. Introduction 2 The impact of logic in Banach space theory 2 The case of model theory 2 Model theory for structures of functional analysis 3 Two famous applications 4 A note on the exposition 4 1. Preliminaries: Banach Space Models 5 Banach space structures and Banach space ultrapowers 5 Positive bounded formulas 7 Approximate satisfaction 8 (1 + )-isomorphism and (1 + )-equivalence of struct...

2007
CHRISTIAN ROSENDAL

We study infinite asymptotic games in Banach spaces with an F.D.D. and prove that analytic games are determined by characterising precisely the conditions for the players to have winning strategies. These results are applied to characterise spaces embeddable into lp sums of finite dimensional spaces, extending results of Odell and Schlumprecht, and to study various notions of homogeneity of bas...

2008
PANDELIS DODOS

We prove a structural property of the class of unconditionally saturated separable Banach spaces. We show, in particular, that for every analytic set A, in the Effros-Borel space of subspaces of C[0, 1], of unconditionally saturated separable Banach spaces, there exists an unconditionally saturated Banach space Y , with a Schauder basis, that contains isomorphic copies of every space X in the c...

2008
Lu-Chuan Ceng Gue Myung Lee Jen-Chih Yao JEN-CHIH YAO

In this paper, we introduce two classes of generalized variational-like inequalities with compositely monotone multifunctions in Banach spaces. Using the KKM-Fan lemma and the Nadler’s result, we prove the existence of solutions for generalized variational-like inequalities with compositely relaxed η − α monotone multifunctions in reflexive Banach spaces. On the other hand we also derive the so...

2009
Alfredo N. Iusem Elena Resmerita

We propose an inexact version of the proximal point method and study its properties in nonreflexive Banach spaces which are duals of separable Banach spaces, both for the problem of minimizing convex functions and of finding zeroes of maximal monotone operators. By using surjectivity results for enlargements of maximal monotone operators, we prove existence of the iterates in both cases. Then w...

2009
Xue-song Li Jong Kyu Kim Nan-jing Huang Charles E. Chidume

We study the strong convergence of two kinds of viscosity iteration processes for approximating common fixed points of the pseudocontractive semigroup in uniformly convex Banach spaces with uniformly Gâteaux differential norms. As special cases, we get the strong convergence of the implicit viscosity iteration process for approximating common fixed points of the nonexpansive semigroup in Banach...

2009
PIOTR KOSZMIDER

We construct an example of a real Banach space whose group of surjective isometries reduces to ± Id, but the group of surjective isometries of its dual contains the group of isometries of a separable infinite-dimensional Hilbert space as a subgroup. To do so, we present examples of extremely non-complex Banach spaces (i.e. spaces X such that ‖ Id+T ‖ = 1+‖T ‖ for every bounded linear operator T...

2002
M. I. Ostrovskii M. I. OSTROVSKII

We consider real spaces only. Definition. An operator T : X → Y between Banach spaces X and Y is called a Hahn-Banach operator if for every isometric embedding of the space X into a Banach space Z there exists a norm-preserving extension T̃ of T to Z. A geometric property of Hahn-Banach operators of finite rank acting between finite-dimensional normed spaces is found. This property is used to ch...

2008
Xin-feng He Yong-chun Xu Zhen He XIN-FENG HE YONG-CHUN XU ZHEN HE

The approximate solvability of a generalized system for nonlinear variational inequality in Hilbert spaces was studied, based on the convergence of projection methods. But little research was done in Banach space. The primary reason was that projection mapping lacked preferably property in Banach space. In this paper, we introduced the generalized projection methods. By using these methods, the...

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