Weakly sequentially continuous differentiable mappings
type: Item
instance of: scholarly article
title: Weakly sequentially continuous differentiable mappings
zbMATH Open document ID: 1191.46034
author: Raffaella Cilia
author: Joaquín M. Gutiérrez
published in: Journal of Mathematical Analysis and Applications
publication date: 2009-11-06T00:00:00Z
review text: The authors consider differentiable mappings \(f:U\subset X \rightarrow Y\), where \(X\) and \(Y\) are real Banach spaces and \(U\) is an open convex subset of \(X\). They characterize the mappings \(f\) which are weakly sequentially continuous in terms of the properties of the derivative \(f':U\subset X \rightarrow \mathcal{L}(X,Y)\). As a consequence, among other results, they obtain differentiable characterizations for the spaces containing no copies of \(\ell_1\) and for the spaces containing \(\ell_1\) and failing the Schur property.
Mathematics Subject Classification ID: 46E50
Mathematics Subject Classification ID: 46G20
Mathematics Subject Classification ID: 46G05
zbMATH DE Number: 5626936
zbMATH Keywords: differentiable mapping
zbMATH Keywords: derivative
zbMATH Keywords: weakly sequentially continuous mapping
zbMATH Keywords: completely continuous mapping
zbMATH Keywords: Banach space not containing \(\ell _{1}\)
zbMATH Keywords: hereditary Dunford-Pettis property
reviewed by: M. González
MaRDI profile type: Publication
full work available at URL: j.jmaa.2009.07.002
OpenAlex ID: W1994565398
cites work: Q4176536
cites work: Estimates by polynomials
cites work: Weakly continuous mappings on Banach spaces
cites work: Polynomial approximation of differentiable functions on Banach spaces.
cites work: Unconditionally converging multilinear operators
cites work: Derivative and factorization of holomorphic functions
cites work: STRONGLY SEQUENTIALLY CONTINUOUS FUNCTIONS
cites work: The hereditary Dunford-Pettis property on C(K,E)
cites work: The Hereditary Dunford-Pettis Property for l 1 (E)
cites work: Q3688914
cites work: Compact factorization of differentiable mappings
cites work: Q4023934
cites work: Smooth noncompact operators from \(C(K)\), \(K\) scattered
cites work: Pyramidal vectors and smooth functions on Banach spaces
cites work: Q3329946
cites work: Q4850055
cites work: Q3281164
cites work: Q3027659
cites work: Functional analysis and infinite-dimensional geometry
cites work: On Completion of Spaces of Weakly continuous Functions
cites work: The compact weak topology on a Banach space
cites work: Weakly Continuous Functions on Banach Spaces not Containing l 1
cites work: Extensions of multilinear operators and Banach space properties
cites work: A counterexample to several questions about Banach spaces
cites work: Smooth functions on \(c_0\)
cites work: Smooth functions on \(C(K)\)
cites work: On \(c_ 0\) sequences in Banach spaces
cites work: Corrigenda to "Differentiable mappings on topological vector spaces" (Studia Math 45(1972),pp. 147-160)
cites work: Compact sets of compact operators in absence of $l^{1}$
cites work: On the Complete Continuity of Differentiable Mappings
cites work: Q5727887
cites work: Q3254563
cites work: Q3294439
cites work: Point-Wise Compact Subsets of the First Baire Class
cites work: Q4340161
cites work: Equicompact sets of operators defined on Banach spaces
cites work: La propriété de Dunford-Pettis dans \(C(K,E)\) et \(L^ 1(E)\)
cites work: Q5734753
cites work: Q4767779
DOI: 10.1016/J.JMAA.2009.07.002
description: scientific article; zbMATH DE number 5626936