Extensions of smooth mappings into biduals and weak continuity
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- Title
- Extensions of smooth mappings into biduals and weak continuity
- Authors
- Choi, YS; Hajek, P; Lee, HJ
- Date Issued
- 2013-02-15
- Publisher
- Elesvier
- Abstract
- Our work is based on a number of tools that are of independent interest. We prove, for every pair of Banach spaces X, Y, that any continuous mapping T : B-X -> Y, which is uniformly differentiable of order up to k in the interior of B-X, can be extended, preserving its best smoothness, into a bidual mapping (T) over tilde : B-X** -> Y**. Another main tool is a result of Zippin's type. We show that weakly Cauchy sequences in X = C(K) can be uniformly well approximated by weakly Cauchy sequences from a certain C[0, alpha], alpha is a countable ordinal, subspace of X**. (C) 2012 Elsevier Inc. All rights reserved.
- Keywords
- Extension to biduals; Dunford-Pettis property; Smoothness; Approximation by polynomials; Reduction lemma; BANACH-SPACES; PROPERTY; APPROXIMATION; SUBSPACES; OPERATORS; C(K)
- URI
- https://oasis.postech.ac.kr/handle/2014.oak/16221
- DOI
- 10.1016/J.AIM.2012.11.001
- ISSN
- 0001-8708
- Article Type
- Article
- Citation
- Advances in Mathematics, vol. 234, page. 453 - 487, 2013-02-15
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