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Extensions of smooth mappings into biduals and weak continuityopen access
- Authors
- Choi, Yun Sung; Hajek, Petr; Lee, Han Ju
- Issue Date
- 15-Feb-2013
- Publisher
- ACADEMIC PRESS INC ELSEVIER SCIENCE
- Keywords
- Extension to biduals; Dunford-Pettis property; Smoothness; Approximation by polynomials; Reduction lemma
- Citation
- ADVANCES IN MATHEMATICS, v.234, pp 453 - 487
- Pages
- 35
- Indexed
- SCI
SCIE
SCOPUS
- Journal Title
- ADVANCES IN MATHEMATICS
- Volume
- 234
- Start Page
- 453
- End Page
- 487
- ISSN
- 0001-8708
1090-2082
- 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.
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Related Researcher
- Lee, Han Ju
- College of Education (Department of Mathematics Education)