scholarly journals On the weak topology of Banach spaces over non-archimedean fields

2011 ◽  
Vol 158 (9) ◽  
pp. 1131-1135
Author(s):  
Jerzy Ka̧kol ◽  
Wiesław Śliwa
Keyword(s):  
Banach Spaces ◽  
Weak Topology

scholarly journals Fixed point theory of Mönch type for weakly sequentially upper semicontinuous maps

2000 ◽  
Vol 61 (3) ◽  
pp. 439-449 ◽  
Author(s):  
Donal O'Regan
Keyword(s):  
Fixed Point ◽  
Differential Equations ◽  
Banach Spaces ◽  
Weak Topology ◽  
Existence Result ◽  
Fixed Point Theory ◽  
Point Theory ◽  
Upper Semicontinuous

A variety of fixed point results are presented for weakly sequentially upper semicontinuous maps. In addition an existence result is established for differential equations in Banach spaces relative to the weak topology.

Banach Spaces which are Radon Spaces with the Weak Topology

1993 ◽  
Vol 25 (6) ◽  
pp. 577-581 ◽  
Author(s):  
Jose L. De Maria ◽  
Baltasar Rodriguez-Salinas
Keyword(s):  
Banach Spaces ◽  
Weak Topology

scholarly journals A Note on the Paper ”Fractional Order Pettis Integral Equations with Multiple Time Delay in Banach Spaces” by M. Benchohra and F.-Z. Mostefai

2015 ◽  
Vol 0 (0) ◽  
Author(s):  
Mieczysław Cichoń
Keyword(s):  
Integral Equation ◽  
Time Delay ◽  
Banach Spaces ◽  
Integral Equations ◽  
Fractional Order ◽  
Weak Topology ◽  
Classical Case ◽  
Existence Results ◽  
Multiple Time ◽  
Pettis Integral

Abstract On a recent paper Benchohra and Mostefai [2] presented some existence results for an integral equation of fractional order with multiple time delay in Banach spaces. In contrast to the classical case, when assumptions are expressed in terms of the strong topology, they considered another case, namely with the weak topology. It has some consequences for the proof. We present here some comments and corrections.

scholarly journals Convex-transitive characterizations of Hilbert spaces

2009 ◽  
Vol 139 (3) ◽  
pp. 633-659 ◽  
Author(s):  
Jarno Talponen
Keyword(s):  
Hilbert Space ◽  
Banach Spaces ◽  
Hilbert Spaces ◽  
Weak Topology ◽  
Linear Projection ◽  
One Dimensional ◽  
Mild Conditions

We investigate real convex-transitive Banach spaces X, which admit a one-dimensional bicontractive projection P on X. Various mild conditions regarding the weak topology and the geometry of the norm are provided, which guarantee that such an X is in fact isometrically a Hilbert space. For example, if uESX is a big point such that there is a bicontractive linear projection P : X → [u] and X* is weak*-locally uniformly rotund, then X is a Hilbert space. The results obtained here are motivated by the well-known Banach—Mazur rotation problem, as well as a question posed by B. Randrianantoanina in 2002 about convex-transitive spaces.

Uniform Kadec–Klee–Huff properties of vector-valued Hardy spaces

1993 ◽  
Vol 114 (1) ◽  
pp. 25-30 ◽  
Author(s):  
P. N. Dowling ◽  
C. J. Lennard
Keyword(s):  
Banach Space ◽  
Banach Spaces ◽  
Hardy Spaces ◽  
Weak Topology ◽  
Uniformly Convex ◽  
Vector Valued

AbstractIn [8] Partington showed that a Banach space X is uniformly convex if and only if Lp([0, 1], X) has the uniform Kadec–Klee–Huff property with respect to the weak topology (UKKH (weak)), where 1 < p < ∞. In this note we will characterize the Banach spaces X such that HP(D, X) has UKKH (weak), where 1 ≤ p < ∞. Similar results for UKKH (weak*) are also obtained. These results (and proofs) are quite different from Partington's result (and proof).

scholarly journals Nuclearity and Banach spaces

1977 ◽  
Vol 20 (3) ◽  
pp. 205-209 ◽  
Author(s):  
Manuel Valdivia
Keyword(s):  
Banach Spaces ◽  
Weak Topology ◽  
Fundamental System ◽  
Nuclear Space ◽  
Infinite Dimensional ◽  
Separable Predual ◽  
Weakly Closed ◽  
The One

SummaryLet E be a nuclear space provided with a topology different from the weak topology. Let {Ai: i ∈ I} be a fundamental system of equicontinuous subsets of the topological dual E' of E. If {Fi: i ∈ I} is a family of infinite dimensional Banach spaces with separable predual, there is a fundamental system {Bi: i ∈ I} of weakly closed absolutely convex equicontinuous subsets of E'such that is norm-isomorphic to Fi, for each i ∈ I. Other results related with the one above are also given.

scholarly journals The fixed-point property in Banach spaces containing a copy ofc0

2003 ◽  
Vol 2003 (3) ◽  
pp. 183-192
Author(s):  
Maria A. Japón Pineda
Keyword(s):  
Banach Space ◽  
Fixed Point ◽  
Banach Spaces ◽  
Weak Topology ◽  
Nonexpansive Mappings ◽  
Fixed Point Property ◽  
Point Property ◽  
Asymptotically Nonexpansive ◽  
Locally Convex Topology ◽  
Locally Convex

We prove that every Banach space containing an isomorphic copy ofc0fails to have the fixed-point property for asymptotically nonexpansive mappings with respect to some locally convex topology which is coarser than the weak topology. If the copy ofc0is asymptotically isometric, this result can be improved, because we can prove the failure of the fixed-point property for nonexpansive mappings.

scholarly journals Unconditionally converging polynomials on Banach spaces

1995 ◽  
Vol 117 (2) ◽  
pp. 321-331 ◽  
Author(s):  
Manuel Gonz´lez ◽  
Joaquín M. Gutiérrez
Keyword(s):  
Banach Space ◽  
Weak Convergence ◽  
Banach Spaces ◽  
Weak Topology ◽  
Linear Operators ◽  
Null Sequence ◽  
Good Tool ◽  
Image Position ◽  
Weakly Unconditionally Cauchy Series ◽  
Cauchy Series

In the study of polynomials acting on Banach spaces, the weak topology is not such a good tool as in the case of linear operators, due to the bad behaviour of the polynomials with respect to the weak convergence. For example,is a continuous polynomial taking a weakly null sequence into a sequence having no weakly Cauchy subsequences. In this paper we show that the situation is not so bad for unconditional series. Recall that is a weakly unconditionally Cauchy series (in short a w.u.C. series) in a Banach space E if for every f ε E* we have that and is an unconditionally converging series (in short an u.c. series) if every subseries is norm convergent.

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