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Extensions of smooth mappings into biduals and weak continuity
- Choi, Yun Sung;
- Hajek, Petr;
- Lee, Han Ju
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5초록
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.
키워드
Extension to biduals; Dunford-Pettis property; Smoothness; Approximation by polynomials; Reduction lemma; BANACH-SPACES; APPROXIMATION; SUBSPACES; OPERATORS
- 제목
- Extensions of smooth mappings into biduals and weak continuity
- 저자
- Choi, Yun Sung; Hajek, Petr; Lee, Han Ju
- 발행일
- 2013-02-15
- 유형
- Article
- 권
- 234
- 페이지
- 453 ~ 487