Denseness of Norm-Attaining Mappings on Banach Spaces
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SCOPUS
- Title
- Denseness of Norm-Attaining Mappings on Banach Spaces
- Authors
- Choi, YS; Lee, HJ; Song, HG
- Date Issued
- 2010-02
- Publisher
- Kyoto University
- Abstract
- Let X and Y be Banach spaces. Let P(X-n : Y) be the space of all Y-valued continuous n-homogeneous polynomials on X. We show that the set of all norm-attaining elements is dense in P(X-n : Y) when a set of use. points of the unit ball B-X is dense in the unit sphere S-X. Applying strong peak points instead of u.s.e. points, we generalize this result to a closed subspace of C-b(M, Y), where M is a complete metric space. For complex Banach spaces X and Y, let A(b)(B-X : Y) be the Banach space of all bounded continuous Y-valued mappings f on B-X whose restrictions f vertical bar(B)degrees(X) to the open unit, ball are holomorphic. It follows that the set of all norm-attaining elements is dense in A(b)(B-X : Y) if the set of all strong peak points in A(b)(B-X) is a norming subset for A(b)(B-X).
- Keywords
- homogeneous polynomial; norm-attaining element; uniformly strongly exposed point; strong peak point; HOLOMORPHIC-FUNCTIONS; MULTILINEAR MAPPINGS; COMPLEX CONVEXITY; THEOREM; POLYNOMIALS
- URI
- https://oasis.postech.ac.kr/handle/2014.oak/27578
- DOI
- 10.2977/PRIMS/4
- ISSN
- 0034-5318
- Article Type
- Article
- Citation
- PUBLICATIONS OF THE RESEARCH INSTITUTE FOR MATHEMATICAL SCIENCES, vol. 46, no. 1, page. 171 - 182, 2010-02
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