The Bishop-Phelps-Bollobas theorem for operators from L(1)(mu) to Banach spaces with the Radon-Nikodym property
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- Title
- The Bishop-Phelps-Bollobas theorem for operators from L(1)(mu) to Banach spaces with the Radon-Nikodym property
- Authors
- Choi, YS; Kim, SK
- Date Issued
- 2011-09-15
- Publisher
- ACADEMIC PRESS INC ELSEVIER SCIENCE
- Abstract
- Let Y be a Banach space and (Omega, Sigma, mu) be a a-finite measure space, where Sigma is an infinite alpha sigma-algebra of measurable subsets of Omega. We show that if the couple (L-1 (mu), Y) has the Bishop-Phelps-Bollobas property for operators, then Y has the AHSP. Further, for a Banach space Y with the Radon-Nikodym property, we prove that the couple (L-1(mu), Y) has the Bishop-Phelps-Bollobas property for operators if and only if Y has the AHSP. (C) 2011 Elsevier Inc. All rights reserved.
- Keywords
- Operator; Norm attaining; Bishop-Phelps theorem; Uniform convexity; NORM ATTAINING OPERATORS
- URI
- https://oasis.postech.ac.kr/handle/2014.oak/17223
- DOI
- 10.1016/J.JFA.2011.05.007
- ISSN
- 0022-1236
- Article Type
- Article
- Citation
- JOURNAL OF FUNCTIONAL ANALYSIS, vol. 261, no. 6, page. 1446 - 1456, 2011-09-15
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