A Nonlinear Transfer Technique for Renorming by Aníbal Moltó, José Orihuela, Stanimir Troyanski, Manuel

By Aníbal Moltó, José Orihuela, Stanimir Troyanski, Manuel Valdivia

Abstract topological instruments from generalized metric areas are utilized during this quantity to the development of in the neighborhood uniformly rotund norms on Banach areas. The ebook deals new strategies for renorming difficulties, them all in keeping with a community research for the topologies concerned contained in the problem.
Maps from a normed area X to a metric house Y, which offer in the neighborhood uniformly rotund renormings on X, are studied and a brand new body for the speculation is got, with interaction among practical research, optimization and topology utilizing subdifferentials of Lipschitz capabilities and overlaying tools of metrization idea. Any one-to-one operator T from a reflexive area X into c0 (T) satisfies the authors' stipulations, shifting the norm to X. however the authors' maps should be faraway from linear, for example the duality map from X to X* supplies a non-linear instance whilst the norm in X is Fréchet differentiable.
This quantity might be attention-grabbing for the vast spectrum of experts operating in Banach area conception, and for researchers in limitless dimensional sensible analysis.

Show description

Read Online or Download A Nonlinear Transfer Technique for Renorming PDF

Similar linear programming books

Practical methods of optimization

Totally describes optimization equipment which are at present most precious in fixing real-life difficulties. considering that optimization has functions in nearly each department of technological know-how and expertise, the textual content emphasizes their sensible elements at the side of the heuristics necessary in making them practice extra reliably and successfully.

Finite Dimensional Variational Inequalities and Complementarity Problems

This complete e-book provides a rigorous and state of the art therapy of variational inequalities and complementarity difficulties in finite dimensions. This category of mathematical programming difficulties presents a strong framework for the unified research and improvement of effective resolution algorithms for quite a lot of equilibrium difficulties in economics, engineering, finance, and technologies.

Parallel Scientific Computing and Optimization: Advances and Applications (Springer Optimization and Its Applications)

This paintings introduces new advancements within the building, research, and implementation of parallel computing algorithms. This booklet offers 23 self-contained chapters, together with surveys, written by way of amazing researchers within the box of parallel computing. each one bankruptcy is dedicated to a few features of the topic: parallel algorithms for matrix computations, parallel optimization, administration of parallel programming versions and knowledge, with the most important specialize in parallel medical computing in business functions.

Semirings and their Applications

There isn't any department of arithmetic, although summary, that could no longer a few day be utilized to phenomena of the genuine international. - Nikolai Ivanovich Lobatchevsky This ebook is an extensively-revised and accelerated model of "The conception of Semirings, with Applicationsin arithmetic and Theoretical laptop technology" [Golan, 1992], first released via Longman.

Additional resources for A Nonlinear Transfer Technique for Renorming

Sample text

Negrepontis [MN92] and the paper of V. Zizler in the Handbook of the Geometry of Banach spaces vol. II [Ziz03], as well as the monographs by R. Deville, G. Godefroy and V. Zizler [DGZ93] and by M. Fabian [Fab97]. Several definitions can be given for this notion (see [Fab97, Chap. 57. A topological space (X, T ) is called K-countably determined if it embeds in a compact space K in such a way that there is a sequence Kn of compact subsets of K such that for every x ∈ X and y ∈ K \ X there exists n0 ∈ N such that x ∈ Kn0 and y ∈ / Kn0 .

4) we get #Vx ≤ ℵ0 . 9) #Zx ≤ ℵ0 . Let x, xn ∈ C0 (Υ) and T xn − T x ∞ → 0. Then supp T x ⊂ T xn . From the definition of Zx we have ∞ m=1 ∞ n=m supp ∞ Zx ⊂ Zxn . 33 as soon as we show that · ∞ . 11) x ∈ spanZx Fix x ∈ C0 (Υ). For ε > 0 set Lε (|x|) = {t ∈ Υ : |x(t)| ≥ ε}, we show that there exists Dx,ε ⊂ Υ such that #Dx,ε < ∞ , Dx,ε ⊂ supp T x , Lε (|x|) ⊂ (0, v] . 12) 38 2 σ-Continuous and Co-σ-continuous Maps Since Lε (|x|) is compact and {(0, v] : v ∈ Lε (|x|)} is an open cover of Lε (|x|) k we can find u1 , u2 , .

X = From the choice of the sets Zx ’s we must have x ∈ Zx so Λx controls x. Moreover let xn ∈ C(K) be a sequence such that Φxn → Φx then x∈ Then ∞ n=1 {Zxn : n ∈ N} = {Mxn : n ∈ N} . Λxn controls x. ii)⇒i). For x ∈ C(K) let Zx := {y ◦ (PΛx K ) : y ∈ C (PΛx K)}. Since PΛx K ⊂ [0, 1]Λx and Λx is countable we have that the space PΛx K is metric so Zx is separable. 33 let us consider a sequence x, xn ∈ C(K) such that lim Φxn = Φx. From ii) it follows that Λ := Λxn controls x so there must exist y ∈ C(PΛ K) such that x = y ◦ (PΛ K ).

Download PDF sample

Rated 4.46 of 5 – based on 42 votes